A food factory produces two kinds of pizza: standard and healthy. The healthy one uses 0.05kg white flour and 0.05kg wholemeal flour, while the standard one uses 0.09kg white flour and 0.01kg wholemeal flour. The company makes £1.2 profit with the standard pizza and £1.6 profit with the healthy pizza. Their supply of white flour is restricted to 4500kg a week, while their supply for wholemeal flour is restricted to 2000kg a week. Using linear programming, find the optimal solution. Then calculate the extra profit or shadow price that can be generated arising from having one more kg of white flour available. Give your result for the shadow price in pounds and to at least 2 decimal places.

A food factory produces two kinds of pizza: standard and healthy. The healthy one uses 0.05kg white flour and 0.05kg wholemeal flour, while the standard one uses 0.09kg white flour and 0.01kg wholemeal flour. The company makes £1.2 profit with the standard pizza and £1.6 profit with the healthy pizza. Their supply of white flour is restricted to 4500kg a week, while their supply for wholemeal flour is restricted to 2000kg a week. Using linear programming, find the optimal solution. Then calculate the extra profit or shadow price that can be generated arising from having one more kg of white flour available. Give your result for the shadow price in pounds and to at least 2 decimal places.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 33P: Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand...

See similar textbooks

Similar questions

Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.
It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.
Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?
A manufacturer has a production facility that requires 10,237 units of component JY21 per year. Following a long-term contract, the manufacturer purchases component JY21 from a supplier with a lead time of 6 days. The unit purchase cost is $31.4 per unit. The cost to place and process an order from the supplier is $168 per order. The unit inventory carrying cost per year is 12.2 percent of the unit purchase cost. The manufacturer operates 250 days a year. Assume EOQ model is appropriate. If the manufacturer uses a constant order quantity of 1,053 units per order, what is the annual holding cost? Use at least 4 decimal places.
The Fish House (TFH) in Norfolk, Virginia, sells fresh fish and seafood. TFH receives daily shipments of farm-raised trout from a nearby supplier. Each trout costs $2.45 and is sold for $3.95. To maintain its reputation for freshness, at the end of the day TFH sells any leftover trout to a local pet food manufacturer for $1.25 each. The owner of TFH wants to determine how many trout to order each day. Historically, the daily demand for trout is: Demand 10 11 12 13 14 15 16 17 18 19 20 Probability 0.02 0.06 0.09 0.11 0.13 0.15 0.18 0.11 0.07 0.05 0.03 a. Construct a payoff matrix for this problem. b. How much should the owner of TFH be willing to pay to obtain a demand forecast that is 100% accurate? give a clear explanation for (b)
Lou Silva has owned and operated The Wellness Store for fifteen years. The company's year-end is December 31st. The following chart lists the company's assets owned prior to 2021 and their UCC balances at the end of 2020. Asset UCC Balance Store (building purchased in 2005) $100,000 Delivery van (Class 10) 15,000 Furniture and office equipment (Class 8) 30,000 Photocopier purchased in 2019 (Separate Class 8) 2,000 Patent (purchased in 2018) 10,000 The following transactions took place in 2021: a. Lou purchased $2,000 worth of small tools (each costing under $500). b. The delivery van was sold for $12,000. The original cost was $20,000. A second-hand van was purchased in the year for $16,000. c. $15,000 was paid for an air conditioning system in the building, which was added to the cost of the standard Class 1 pool. d. Lou sold the photocopier for $1,500 in the year, and will replace it in January 2022 with a second-hand model valued…
HERO Corporation is considering three options for managing its data processing operation: continuing with its own staff, hiring an outside vendor to do the managing (referred to as outsourcing), or using a combination of its own staff and an outside vendor. The cost of the operation depends on future demand. The annual cost of each option (in thousands of pesos) depends on demand as follows: Demand Demand Demand Staffing Options High Medium Low Own staff 352 325 300 Outsider vendor 450 300 150 Combination 400 325 250 If the decision maker knows nothing about the probabilities of the four states of nature, what is the recommended decision using:i. the optimistic approach and the conservative approach iii. the minimax regret approach iv. the Laplace method
A company owns a 5-year-old turret lathe that has a book value of $23,000. The present market value for the lathe is $18,000. The expected decline in market value is $1,700/year to a minimum market value of $4,080; maintenance plus operating costs for the lathe equal $4,470/year.A new turret lathe can be purchased for $46,000 and will have an expected life of 8 years. The market value for the turret lathe is expected to equal $46,000(0.70)k at the end of year k. Annual maintenance and operating cost is expected to equal $1,900. Based on a 12% MARR, should the old lathe be replaced now? Use an equivalent uniform annual cost comparison, a planning horizon of 7 years, and the cash flow approach.EUAC for keeping old turret lathe: $EUAC for replacing turret lathe: $
The ABC Corporation has been engaged in the manufacture of electronic components for automobiles for the last five years. The company employees 350 employees and about 30 supervisors and managers. The increase in technology requires that employees be sent to cope with the increasing demand for updated new products consistent with the demand of local and foreign customers. The HR Manager suggested that three of the managers and eight supervisors be sent to the mother company in Japan for updates in technology on car electronics. The Vice President for Finance and the Operation Manager opposed the recommendation on the basis of cost-cutting and lack of personnel to handle the operations while they were asway for two months. They suggested that technicians from the mother company be invited instead to handle the training in the Philippines. The cost of training by the mother company would double the cost of training as they are paid higher allowances and salaries that will be charged to…
Assuming your company is producing Apple and Samsung phone cases. It is required to process in the assembly and paint shops to make either phone case. It takes 1/60 of a day and 1/40 of a day to paint an Apple case and a Samsung case in the paint shop, respectively. It takes 1/50 of a day to assemble either type of case in the assembly shop. An Apple phone case and a Samsung phone case yield profits of $300 and $220, respectively, per case sold. What is a maximum-profit daily production plan for your company?
The Marketing Manager of Dotcom Limited has conducted a market research on the price-demand relationship for its consumer durable Product-V which has been recently launched. The price-demand pattern will be as follows: Price per unit (Rs.) 16.650 16.050 14.400 13.050 Product-V is manufactured in batches of 1.000 units. The production manager of Dotcom Limited has also researched and studies the pattern and believes that 50% of the variable manufacturing cost would have a learning effect. This learning curve effect will continue up to 4.000 units of production at constant rate But after 4.000 units of production unit variable manufacturing cost would be equal to the unit cost at the 4 batch. The manufacturing unit cost of the first batch will be Rs. 6.600 of which only 50% is subjected to learning and experience curve effect. The average unit variable of all 4 batches will be Rs 6.180 The price and maximum contribution at which Dotcom Limited should sell Product-V is: Rs.14,400, Rs.…
4) The making of rivet holes in structural steel members can be done by 2 methods. The first method consists of laying out the position of the holes in the members and using a drill press costing P100k. The machinist is paid P60 per hour and he can drill 80 holes per hour. The second method makes use of a multiple-punch machine costing P80k. The punch operator is paid P40 an hour and he can punch out 1 hole for 3 seconds. This method also requires an expense of P1.25 per hole to set the machine. (a) if all other costs are assumed equal, what is the total cost for each machine for 10k holes, assuming the total cost of each machine to be charged to these holes? (b) for how many holes will the costs be equal?