Concept explainers
Explanation of Solution
Formulation of a Linear
Let consider “xs1” and “xs2” be the number of pounds of silicon used in fertilizer 1 and fertilizer 2.
Let “xn1” and “xn2” be the number of pounds of nitrogen used in fertilizer 1 and fertilizer 2.
The objective is to maximize the profits of Bullco.
Therefore, the objective function is,
Maximum
Constraint 1:
At most, 100lb of silicon can be purchased.
Amount of silicon used to produce fertilizer 1 and 2
Constraint 2:
At most, 80lb of nitrogen can be purchased
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Chapter 3 Solutions
Operations Research : Applications and Algorithms
- ACE Hardware wants to develop a daily schedule for its employees in one of its stores in Omaha. Currently,this store has five employees and the store is opened from 12pm to 9pm. The store must always have at leasttwo people on hand. Each employee must work at least four hours and no more than eight hours per day.Employee #1 goes to school and cannot start before 4pm while all other employees can work at any time.Furthermore, employee #1 earns $10 per hour while all other employees earn $12 per hour. Because all fiveemployees live so close to the store, you must assume that they do not need to work consecutive hours.a) Formulate an optimization model for this problem.b) Solve the optimization model using either the Microsoft Excel Solver or the IBM ILOG CPLEXOptimization Studio.arrow_forwardWilson Creek Farm has 200 acres of land available for planting. The owner is considering planting three crops: corn, soybeans, and wheat. The production yield, water requirements, and labor requirements for a salable crop are given here. The owner expects to have only 35,000 gallons of water available per week to use for the crops, and during the growing season he will only have 8000 person-hours of labor available. The expected profit per bushel of each crop is $1.00 for corn, $1.60 for soybeans, and $3.00 for wheat. The owner can use any mix of crops (i.e., he can plant the same crop on all 200 acres or he can plant all three crops in different proportions). d. Solve the problem using Excel Solver Tool. Add supporting pictures from the software for each step. Discuss your output in line with the given reports from Excel. Bushels/ Acre Water Required Produced (gal/acre/week) Crop 300 Corn Soybeans 200 Wheat 80 200 150 125 Person-Hours Labor Required/Acre 35 40 30arrow_forwardTruckco manufactures two types of trucks: 1 and 2. Each truck must go through the painting shop and assembly shop. If the painting shop were completely devoted to painting Type 1 trucks, then 800 per day could be painted; if the painting shop were completely devoted to painting Type 2 trucks, then 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, then 1,500 per day could be assembled; if the assembly shop were completely devoted to assembling truck 2 engines, then 1,200 per day could be assembled. Each Type 1 truck contributes $300 to profit; each Type 2 truck contributes $500. How much capacity in percent does a single truck of each type uses at each shop?arrow_forward
- Pneumatics Engineering purchased a machine that had a fi rst cost of $40,000, an expected useful life of 8 years, a recovery period of 10 years, and a salvage value of $10,000. The operating cost of the machine is expected to be $15,000 per year. The inflation rate is 6% per year and the company’s MARR is 11% per year. Determine the depreciation charge for year 3 according to the straight line method. (UNITS ARE REQUIRED)arrow_forwardAt the beginning of month 1, Finco has $400 in cash. At the beginning of months 1, 2, 3, and 4, Finco receives certain revenues, after which it pays bills (see Table 2 below). Any money left over may be invested for one month at the interest rate of 0.1% per month; for two months at 0.5% per month; for three months at 1% per month; or for four months at 2% per month. Use linear programming to determine an investment strategy that maximizes cash on hand at the beginning of month 5. Formulate an LP to maximize Finco’s profit.arrow_forwardLeary Chemical manufactures three chemicals: A, B, and C. These chemicals are produced via two production processes: 1 and 2. Running process 1 for an hour costs $4 and yields 3 units of A, 1 of B, and 1 of C. Running process 2 for an hour costs $1 and produces 1 unit of A and 1 of B. To meet customer demands, at least 10 units of A, 5 of B, and 3 of C must be produced daily. Processes cannot be run simultaneously, and total number of operational hours is limited to 12 hours. Construct an LP model to determine a daily production plan that minimizes the cost of meeting Leary Chemical’s daily demands.arrow_forward
- At the beginning of month 1, Finco has $400 in cash. At the beginning of months 1, 2, 3, and 4, Finco receives certain revenues, after which it pays bills (see Table 2 below). Any money left over may be invested for one month at the interest rate of 0.1% per month; for two months at 0.5% per month; for three months at 1% per month; or for four months at 2% per month. Use linear programming to determine an investment strategy that maximizes cash on hand at the beginning of month 5. Formulate an LP to maximize Finco’s profit. Table 2 Month Revenues ($) Bills ($) 1 400 600 2 800 500 3 300 500 4 300 250arrow_forwardProblem 5. An Electricity board charges the following rates mentioned in the table for the use of electricity. All users are charged Taka 50 as a meter charge for every month. If any user wants to change/replace his meter, he will be charged taka 2000. The monthly bill will be generated based on ● Customer Category ● Consumed Units ● Phase ● For Category 3 and 5 along with other parameters, you need to also consider flat rate, peak time, and off-peak time. Take input from the user, how many units were consumed during flat rate, peak, or off-peak time. ● Meter Charge Write a program to read the name of the user, Customer Category, Phase, number of units consumed and print out the monthly bill. Note that ● Phase, flat rate, peak time and off-peak time will be appeared based on the customer category. ● The monthly bill will be calculated following the number of Days in a montharrow_forwardA company manufactures two types of trucks. Each truck must go through the painting shop and the assembly shop. If the painting shop were completely devoted to painting type 1 trucks, 800 per day could be painted, whereas if the painting shop were completely devoted to painting type 2 trucks, 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, 1500 per day could be assembled, whereas if the assembly shop were completely devoted to assembling truck 2 engines, 1200 per day could be assembled. It is possible, however, to paint both types of trucks in the painting shop. Similarly, it is possible to assemble both types in the assembly shop. Each type 1 truck contributes $1000 to profit; each type 2 truck contributes $1500. Use Solver to maximize the company’s profitarrow_forward
- The public utilities commission has decided that the electric company overcharged its customers for two months last year. To make up the difference to the customers, the commission orders the company to decrease each of the next month’s bills by 10%. The city also levies a 3%utility tax, which is to be applied to the bill before it is discounted. Also, the10% discount does not apply to the utility tax. Assume electricity costs $0.16per kilowatt-hour. Write a program to compute the next month’s electricity bill given the number of kilowatt-hours consumed as inputarrow_forwardABC Company produces three electrical products—blenders, choppers, and toasters. The manufacturer has a maximum daily production budget of RM2000 and a maximum of 660 hours of labor. Maximum daily customer demand is for 200 blenders, 300 choppers, and 150 toasters. The unit profit for blender is RM8, choppers, RM10, and toaster, RM7. The company desires to know the optimal product mix that will maximize profit. These products have the following resource requirements as shown in Table 1. Based on the report, answer the following questions and justify all your answers. Formulate the LP model for the above case study. Suppose that the company would like to increase the profit of the toasters to RM9 per unit without affecting the optimum number of products to be produced based on earlier conditions. Based on the Sensitivity Report, advise the company if this can be accomplished and justify your answer. If this can be done, what would be the company’s profit based on new pricing. The…arrow_forwardABC Company produces three electrical products—blenders, choppers, and toasters. The manufacturer has a maximum daily production budget of RM2000 and a maximum of 660 hours of labor. Maximum daily customer demand is for 200 blenders, 300 choppers, and 150 toasters. The unit profit for blender is RM8, choppers, RM10, and toaster, RM7. The company desires to know the optimal product mix that will maximize profit. These products have the following resource requirements as shown in Table 1. Based on the report, answer the following questions and justify all your answers. Formulate the LP model for the above case study. Optimize the Company ABC production using linear programming simplex method. Suppose that the company would like to increase the profit of the toasters to RM9 per unit without affecting the optimum number of products to be produced based on earlier conditions. Based on the Sensitivity Report, advise the company if this can be accomplished and justify your answer. If this…arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole