A community council must decide which recreation facilities to construct in its community. Five new recreation facilities have been proposed - a soccer field (xs), an athletic field (xa), a gymnasium (xg). a swimming pool (xp), a tennis center (xp). The council wants to select facilities that will maximize the expected daily usage by the residents of the community, subject to budget and selection limitations. The expected daily usage and cost information for each facility are given below: Recreation Facility Expected Usage (people/day) Cost (S in K) Soccer field 180 50 Athletic field 130 20 Gymnasium 240 85 Swimming pool 270 40 Tennis center 70 15 The community has a $140K construction budget. The selection must also comply with the following two criteria: (1) At least two of the proposed facilities must be selected; and (2) gymnasium and tennis center cannot be selected simultaneously. Fill in the blanks to complete the formulation for this 0-1 integer programming model that maximizes the expected usage. You should type the missing coefficient values. (Hint: If a variable should not appear in a constraint, then you should type 0 for its coefficient value.) Max Z = 180 xg+ 130 xa + 240 xg + Xp + st. 50 xs + 20 xa + Xg + Xp + 15 x4s 140 1 xg + 1 xg + 1 xg + 1 xXp + 1 x¢2 Xa+ Xg+ Xp+ Xj is binary for all i

A community council must decide which recreation facilities to construct in its community. Five new recreation facilities have been proposed - a soccer field (xs), an athletic field (xa), a gymnasium (xg). a swimming pool (xp), a tennis center (xp). The council wants to select facilities that will maximize the expected daily usage by the residents of the community, subject to budget and selection limitations. The expected daily usage and cost information for each facility are given below: Recreation Facility Expected Usage (people/day) Cost (S in K) Soccer field 180 50 Athletic field 130 20 Gymnasium 240 85 Swimming pool 270 40 Tennis center 70 15 The community has a $140K construction budget. The selection must also comply with the following two criteria: (1) At least two of the proposed facilities must be selected; and (2) gymnasium and tennis center cannot be selected simultaneously. Fill in the blanks to complete the formulation for this 0-1 integer programming model that maximizes the expected usage. You should type the missing coefficient values. (Hint: If a variable should not appear in a constraint, then you should type 0 for its coefficient value.) Max Z = 180 xg+ 130 xa + 240 xg + Xp + st. 50 xs + 20 xa + Xg + Xp + 15 x4s 140 1 xg + 1 xg + 1 xg + 1 xXp + 1 x¢2 Xa+ Xg+ Xp+ Xj is binary for all i

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section5.3: Assignment Models

Problem 12P

See similar textbooks

Similar questions

Mick Karra is the manager of MCZ Drilling products which produces a variety of especially valves for oil field equipment. Recent activity in the oil fields has cause demand to increase drastically, and a decision has been made to open a new manufacturing facility. Three locations are being considered, and the size of the facility would not be the same in each location Thus, overtime might be necessary at times. The folowing table gives the total monthly cost (in 1000s) for each possible location under each demand posibility. The probabilities for the demand levels have been determined to be 20% for low demand, 30% for medium demand, and 50% for high demand Demand is Low Demand is medium Demand is High Ardmore, OK 85 110 150 Sweetwater, TX 90 100 120 Lake Charles, LA 110 120 130 (a) Which location would be selected based on the optimistic criterion? (b) which location would be selected based on the pessimistic criterion? (c) which location would be selected based on the…
The Candle Company plans to open a new retail store in Portland, Maine. The store will sell specialty candles for an average of $10 each. The average variable costs per candle are as follows: Wax $4 Other additives $2 Base $1 The company is negotiating its lease for the new location. The landlord has offered two leasing options: Option A) a lease of $2,500 per month; or Option B) a monthly lease cost of $2,000 plus 10% of the company's monthly sales revenue. The lease option that is more attractive for the company under its current sales expectations is option B, the fixed lease payment plus sales based commission because it results in the lowest total lease costs The indifference point is The company expects to sell approximately 400 candles per month. Requirement 2. At what level of sales (in units) would the company be indifferent between the two lease options? Show your proof. candles. Begin by selecting the equation to determine the indifference point. (Abbreviations used" FC =…
2. Garysburg Fire Rescue (GFR) is considering three different locations for a new fire station. Using factor rating, GFR has created the following table. When rating these locations, GFR used a 5- point scale, where 1 means unfavorable and 5 means excellent. (Noteshaper Scenario #26) Factor Weight Location 1 Location 2 Location 3 Cost of land 0.5 4 1 Accessibility 0.3 2 2 4 Size of Land 0.2 1 3 3 a. Which of the following statements are true and which are false? I. The cost of the available land parcel is of the greatest importance in this analysis. I. Location 2 has better accessibility than location 3. GFR considers the size of the available land parcel to be the least important III. factor.
A local restaurateur, Cho Senn, is considering three options for his new Asian fusic restaurant. Option A - called Midtown - will have annual fixed costs of 42,500 an variable costs of 3.45 per customer. Option B - called Market - will have annual fixed costs of 30,000 and variable costs of 4.40 per customer. Finally Option C - called Mall has annual fixed cost of 19,500 and variable costs of 5.25 per customer. If Mr. Cho averages 8.25 in revenue per customer, what volume is required to breakeven with Option B? Your Answer: - Answer 4
Cost Allocation Problem The housekeeping services department of Ruger Clinic, amultispecialty practice, had $100,000 in direct costs in 2020. These costs must be allocated to Ruger’s three revenue-producing patient services departments using the direct method. Two cost drivers are under consideration: patient services revenue and hours of housekeeping services used. The patient services departments generated $5 million in total revenues during 2020, and to supportthese clinical activities, they used 5,000 hours of housekeeping services. What is the value of the cost pool? What is the allocation ratio if patient services revenue is used as the cost driver? hours of housekeeping services is used as the cost driver? Assume that the three patient services departments are adult services, pediatric services, and other services. The patient services revenue and hours of housekeeping services for each department are as follows: Department Revenue…
Problems 2 Helen Murvis, hospital administrator for Portland General Hospital, is trying to determine whether to build a large wing onto the existing hospital, a small wing, or no wing at all. If the population of Portland continues to grow, a large wing could return $150,000 to the hospital each year. If the small wing were built, it would return S$60,000 to the hospital each year if the population continues to grow. If the population of Portland remains the same, the hospital would encounter a loss of $85,000 if the large wing were built. Furthermore, a loss of $45,000 would be realized if the small wing were constructed and the population remains the same. Unfortunately, Helen does not have any information about the future population of Portland * Develop a decision table for this problem. * Determine the best decision using the following decision criteria 1. Мaximax 2. Маximin 3. Minimax Regret Hurwicz (use a coefficient of realism of 0.75) 5. Equal likelihood 6. Expected Value 7.…
A health centre specializes in the provision of sports/exercise and medical/dietary advice to clients. The service is provided on a residential basis and clients may stay for whatever number of days to suit their needs. Budgeted estimates for the year ending 30 June 2020 are as follows: (i) The maximum capacity of the centre is 50 clients per day for 350 days in a year. (ii) Clients will be invoiced at a fee per day. The budgeted occupancy level will vary with the client fee level per day and is estimated at different percentages of maximum capacity as follows: Client fee per day Occupancy level Occupancy as percentage of maximum capacity RM180 High 90% RM200 Most likely 75% RM220 Low 60% (iii) Variable costs are also estimated at one of three levels per client day. The high, most likely and low levels per client day are RM95, RM85 and RM70 respectively. The range of cost levels reflects only the possible effect of the purchase prices of goods…
A flood control reservoir project and channel improvement project are proposed for reducing flood damages along a stream in an urban area. Estimated costs are as follows: Dam and reservoir project Channel improvement project Initial investment $1,500,000 $1,200,000 Annual maintenance $10,000/yr $5,000/yr Hydrologic, hydraulic and economic studies have been conducted to develop the following relationships for the river reach and flood plain: (a) annual exceedance probability versus peak discharge with and without the reservoir, (b) discharge versus stage with and without the channel improvement, and (c) stage versus damage Annual Peak discharge Stage (ft) exceedance (cfs) probability Without With Discharge reservoir reservoir (cfs) Without With Stage Damage project project (ft) million) 0.50 3,000 2,700 0 0 0 9 0.0 0.20 5,400 0.10 7,600 4,200 3,500 5,000 10. 7 10 0.2 10,000 15° 11 15 1.1 0.05 10,400 5,500 15,000 20 14 20 2.2 0.02 0.01 19,000 0.005 24,000 20,000 15,000 8,600 20,000 23 17…
Dawson Electronics is a manufacturer of high-tech control modules for lawn sprinkler systems. Denise, the CEO, is trying to decide if the company should develop one of the two potential new products, the Water Saver 1000 or the Greener Grass 5000. With each product, Dawson can capture a bigger market share if it chooses to expand capacity by buying additional machines. Given different demand scenarios, their probabilities of occurrence, and capacity expansion versus no change in capacity, the potential sale of each product are summarized in the included table. Click the icon to view the table. What is the expected payoff for the Water Saver 1000 and the Greener Grass 5000, with and without capacity expansion? The expected payoff for the Water Saver 1000 with the capacity expansion is $ integer.) The expected payoff for the Water Saver 1000 without the capacity expansion is $. (Enter your response as an integer.) ਗਿਆ (Enter your response as an The expected payoff for the Greener Grass…
Fort Wayne Plastics Inc is trying to develop a plan for its workforce and production levels for the six-month period from January to June. The firm produces plastic components. Forecast demands over the next six months are 1,304, 633, 809, 1,175, 2,146, and 1,373. There are currently (end of December) 347 workers employed in the plant. Ending inventory in December is expected to be 461 units, and the firm would like to have 575 units on hand at the end of June. The cost of hiring one worker is $546. The cost of firing a worker is $900. The cost of holding one unit of inventory for one month is $60. In the past, the plant manager observed that over 21 working days, with the workforce level constant at 76 workers, the firm produced 233 plastic components. The number of working days per month from January to June for this year is 26, 25, 25, 17, 22, 17. Find the optimal production per month as well as the corresponding optimal cost for this plan. P1 Number P2= Number P3 Number P4 Number…
A council has a brown-field sites designated for social housing. After allowing for roads and parks it has an area of 150000 m² for social housing. The housing association intends to build a mixture of flats, two-bedroom houses, three-bedroom houses, and shops (which include a living space) on this site. The housing association wishes to maximise the number of people that can be housed but has strict housing requirements: • there must be at least twice as many two-bedroom houses as three-bedroom houses; • at least 10% of the total housing units excluding shops (i.e. flats and houses) must be flats; • buildings containing the flats (i.e a "block") must have two storeys and every flat must have the same floor space; • shops must be provided at a rate of at least one per 1500 inhabitants. The average number of inhabitants per housing unit and the ground floor area of each are given in the following table. Housing type Flat Two-bedroom house Three-bedroom house Shop Average number of…
Two vaccination schemes are recently adopted in Lebanon, Pfizer and Astrazenica The profit for each one of these is dependent on the site (clinic or hospital) performing the vaccination process. This is shown in the following payoff table. Ministry of health considering the maximum profit to be able to cover the cost of staff where vaccination process can either be in a small clinics, or medium size hospitals or in main hospitals Alternative capacity for new store Pfizer Astrazenica Clinics 10 Small Hospitals Main Hospitals 7 6. 3 (a) Assume the payoffs represent profits. Determine the alternative that would be chosen under each of these decision criteria: Maximin, Maximax, Laplace, In your own opinion, which alternative likely to be excluded and why? (b) The ministry of health would like to check the possible loss. Find out the minimax regret table and identify the recommended alternative. (c) Assuming the probability of getting Pfizer is 0.6 and getting Astrazenica is 40%, determine…