A factory manufactures three products, A, B, and C. Each product requires the use of two machines, Machine I and Machine II. The total hours available, respectively, on Machine I and Machine II per month are 7,050 and 9,340. The time requirements and profit per unit for each product are listed below. A B C Machine I 4 9. 11 Machine II 8 7 16 Profit $10 $12 $14 How many units of each product should be manufactured to maximize profit, and what is the maximum profit? Start by setting up the linear programming problem, with A, B, and C representing the number of units of each product that are produced. Maximize P subject to: s7,050 < 9,340 Enter the solution below. If needed round numbers of items to 1 decimal place and profit to 2 decimal places. The maximum profit is $ when the company produces: units of product A units of product B units of product C

A factory manufactures three products, A, B, and C. Each product requires the use of two machines, Machine I and Machine II. The total hours available, respectively, on Machine I and Machine II per month are 7,050 and 9,340. The time requirements and profit per unit for each product are listed below. A B C Machine I 4 9. 11 Machine II 8 7 16 Profit $10 $12 $14 How many units of each product should be manufactured to maximize profit, and what is the maximum profit? Start by setting up the linear programming problem, with A, B, and C representing the number of units of each product that are produced. Maximize P subject to: s7,050 < 9,340 Enter the solution below. If needed round numbers of items to 1 decimal place and profit to 2 decimal places. The maximum profit is $ when the company produces: units of product A units of product B units of product C

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section6.4: Fixed-cost Models

Problem 18P

See similar textbooks

Similar questions

Chemco produces three products: A, B, and C. Theycan sell up to 30 pounds of each product at the followingprices (per pound): product A, $10; product B, $12; productC, $20. Chemco purchases raw material at $5/lb. Each poundof raw material can be used to produce either 1 lb of A or1 lb of B. For a cost of $3/lb processed, product A can beconverted to .6 lb of product B and .4 lb of product C. Fora cost of $2/lb processed, product B can be converted to.8 lb of product C. Formulate an LP whose solution will tellChemco how to maximize their profit
Capsule Drugs manufactures two drugs. The drugs areproduced by blending two chemicals. By weight, drug 1must contain at least 65% chemical 1, and drug 2 mustcontain at least 55% chemical 1. Drug 1 sells for $6 perounce, and drug 2 sells for $4 per ounce. Chemicals 1and 2 can be produced by one of two production processes. Running process 1 for an hour requires 7 ouncesof raw material and 2 hours of skilled labor, and ityields 3 ounces of each chemical. Running process 2 foran hour requires 5 ounces of raw material and 3 hoursof skilled labor, and it yields 3 ounces of chemical 1 and1 ounce of chemical 2. A total of 3000 hours of skilledlabor and 5000 ounces of raw material are available.Determine how to maximize Capsule’s sales revenues.
Globex Investment Capital Corporation owns six companies that have the following estimatedreturns (in millions of dollars) if sold in one of the next 3 years:Year Sold(Estimated return, $1,000,000s)Company 1 2 31 14 18 232 9 11 153 18 23 274 16 21 255 12 16 226 21 23 28To operating funds, the company must sell at least $24 million worth of assets in year 1, $28million in year 2, and $32 million in year 3. Globex wants to develop a plan for selling thesecompanies during the next 3 years to maximize return.(a) Formulate an integer programming model for this problem.
Shoemakers of America forecasts the following demandfor each of the next six months: month 1—5,000 pairs;month 2—6,000 pairs; month 3—5,000 pairs; month 4—9,000 pairs; month 5—6,000 pairs; month 6—5,000 pairs. Ittakes a shoemaker 15 minutes to produce a pair of shoes.Each shoemaker works 150 hours per month plus up to 40hours per month of overtime. A shoemaker is paid a regularsalary of $2,000 per month plus $50 per hour for overtime.At the beginning of each month, Shoemakers can either hireor fire workers. It costs the company $1,500 to hire a workerand $1,900 to fire a worker. The monthly holding cost perpair of shoes is 3% of the cost of producing a pair of shoeswith regular-time labor. (The raw materials in a pair of shoescost $10.) Formulate an LP that minimizes the cost ofmeeting (on time) the demands of the next six months. Atthe beginning of month 1, Shoemakers has 13 workers
Shoemakers of America forecasts the following demandfor each of the next six months: month 1—5,000 pairs;month 2—6,000 pairs; month 3—5,000 pairs; month 4—9,000 pairs; month 5—6,000 pairs; month 6—5,000 pairs. Ittakes a shoemaker 15 minutes to produce a pair of shoes.Each shoemaker works 150 hours per month plus up to 40hours per month of overtime. A shoemaker is paid a regularsalary of $2,000 per month plus $50 per hour for overtime.At the beginning of each month, Shoemakers can either hireor fire workers. It costs the company $1,500 to hire a workerand $1,900 to fire a worker. The monthly holding cost perpair of shoes is 3% of the cost of producing a pair of shoeswith regular-time labor. (The raw materials in a pair of shoescost $10.) Formulate an LP that minimizes the cost of At the conclusion of the season, this method has beenused to determine ratings for college football and collegebasketball. What problems could be foreseen if this methodwere used to rate teams early in the…
The board of directors of General Wheels Company is considering seven large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit (net present value) that they will generate as well as in the amount of capital required, as shown by the following table. Investment Opportunity 1 2 3 4 5 6 7 Estimated Profit ($million) 17 10 15 19 7 13 9 Capital Required for Investment Opportunity ($million) Capital Available ($million) 1 2 3 4 5 6 7 Capital 43 28 34 48 17 32 23 100 The total amount of capital available for these investments is $100 million. Investment opportunities 1 and 2 are mutually exclusive, and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken unless one of the first two opportunities is undertaken. There are no such restrictions on investment opportunities 5, 6, and 7. The objective is to select the combination of capital investments that will maximize the total estimated long-run…
A manufacturer can sell product 1 at a profit of $2/unitand product 2 at a profit of $5/unit. Three units of rawmaterial are needed to manufacture 1 unit of product 1, and6 units of raw material are needed to manufacture 1 unit ofproduct 2. A total of 120 units of raw material are available.If any of product 1 is produced, a setup cost of $10 isincurred, and if any of product 2 is produced, a setup costof $20 is incurred. Formulate an IP to maximize profits.
Daisy Drugs manufactures two drugs: 1 and 2. Thedrugs are produced by blending two chemicals: 1 and 2. Byweight, drug 1 must contain at least 65% chemical 1, anddrug 2 must contain at least 55% chemical 1. Drug 1 sellsfor $6/oz, and drug 2 sells for $4/oz. Chemicals 1 and 2 canbe produced by one of two production processes. Runningprocess 1 for an hour requires 3 oz of raw material and 2hours skilled labor and yields 3 oz of each chemical.Running process 2 for an hour requires 2 oz of raw materialand 3 hours of skilled labor and yields 3 oz of chemical 1and 1 oz of chemical 2. A total of 120 hours of skilled laborand 100 oz of raw material are available. Formulate an LPthat can be used to maximize Daisy’s sales revenues
A company manufactures Products A, B, and C. Each product is processed in three departments: I, II, and III. The total available labor-hours per week for Departments I, II, and III are 780, 900, and 720, respectively. The time requirements (in hours per unit) and the profit per unit for each product are as follows. ProductA ProductB ProductC Dept. I 2 1 2 Dept. II 3 1 2 Dept. II 2 2 1 Profit $18 $12 $15 If management decides that the number of units of Product B manufactured must equal or exceed the number of units of products A and C manufactured, how many units of each product should the company produce to maximize its profit? product A product B product C What is the maximum profit (in dollars)?
DynaTune is trying to determine how to allocate its $145,000advertising budget for a new product. Radio and television arethe two media outlets selected for advertising. Th e followingtable shows the costs of advertising in these two media and theestimated number of new customers reached by increasingamounts of advertising For example, each of the fi rst 10 ads the company places on theradio will cost $1000 and is expected to reach 900 new customers.Each of the next 10 will cost $900 and is expected to reach 700new customers. Assume the company will purchase no more than30 radio ads and no more than 15 television ads.(a) Formulate an LP to maximize the number of newcustomers reached.(b) Set up and solve the problem on a spreadsheet.(c) What is the optimal solution? Explain the rationale for thesolution.(d) Suppose the number of new customers reached by 11–15television ads is 7500 and the number reached by 6–10ads is 5000. Resolve the problem. What is wrong with thissolution? Is Solver…
Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows:Department Product 1 Product 2 Product 3A 1.5 3 2B 2 1 2.5C 0.25 0.25 0.25During the next production period the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $25 for product 1, $28 for product 2, and $30 for product 3. a. Formulate a linear programming model for maximizing total profit contribution. b. Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution?c. After evaluating the solution obtained in part (b), one of the production supervisors noted that production setup costs had not been taken into account. She noted that setup costs are $400 for product 1, $550 for product 2, and $600 for product 3. If the solution developed in part…
Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 5R + 8C s.t. R + 3 2 C ≤ 800 Cutting and sewing 1 2 R + 1 3 C ≤ 240 Finishing 1 8 R + 1 4 C ≤ 100 Packaging and shipping R, C ≥ 0 The computer solution is shown below. Optimal Objective Value = 3520.00000 Variable Value Reduced Cost R 320.00000 0.00000 C 240.00000 0.00000 Constraint Slack/Surplus Dual Value 1 120.00000 0.00000 2 0.00000 3.00000 3 0.00000 28.00000 Variable ObjectiveCoefficient AllowableIncrease AllowableDecrease R 5.00000 7.00000 1.00000 C 8.00000 2.00000 4.66667 Constraint RHSValue AllowableIncrease AllowableDecrease 1 800.00000 Infinite 120.00000 2 240.00000 160.00000 106.66667 3…