A company makes two products (Table and Chair) using two machines (A and B). Each unit of tablethat is produced requires 50 minutes processing time on machine A and 30 minutes processingtime on machine B. Each unit of Chair that is produced requires 24 minutes processing time onmachine A and 33 minutes processing time on machine B. Below are the relevant data for Tablesand Chairs:PRODUCTSTOCKS ONTHECURRENTWEEKFORECASTEDDEMANDTABLES3075CHAIRS9095Available processing time on machine A is forecast to be 40 hours and on machine B is forecastto be 35 hours. Company policy is to maximize the combined sum of the units of Tables and theunits of Chairs in stock at the end of the week.REQUIRED:a. Formulate the problem of deciding how much of each product to make in the currentweek as a linear program.b. Solve this linear program graphically.

Answered: a. Formulate the problem of deciding…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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The Ace Manufacturing Company has orders for three similar products. Product Min A s.t. B C 1 2 Machine 3 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. A A LB B Ic C Product 4 2 3 Orders (units) Machine 1 Capacity Product A Orders Machine 2 Capacity Product B Orders Machine 3 Capacity Product C Orders 1,800 X20 for all i, j. 700 1,100 Capacity (units) 1,400 (a) Develop the linear programming formulation of this problem. (Let x₁ be the number of units of product A produced by XA1 machine 1, x,, be the number of units of product i produced by machine j, etc.) 1,500 1,000 1 Machine $1.00 $1.30 $1.10 2 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20 3 (b) Solve the transportation model for the…
a. Identify the feasible solution. b. Obtain the optimal solution. Note: Assumer or determine the objective function from available data.
A linear programming computer package is needed. The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown. Constraint Television Radio Online Audience per advertisement 400,000 72,000 160,000 Cost per advertisement $2,000 $300 $600 Maximum media usage 10 20 10 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. If the promotional budget is limited to $20,500, By how much would audience contact increase if an extra $100 were allocated to the promotional budget? (Round your answer to the nearest whole number.)
Green Vehicle Inc., manufactures electric cars and small delivery trucks. It has just opened a new factory where the C1 car and the T1 truck can both be manufactured. To make either vehicle, processing in the assembly shop and in the paint shop are required. It takes 1/25 of a day and 1/60 of a day to paint a truck of type T1 and a car of type C1 in the paint shop, respectively. It takes 1/45 of a day to assemble either type of vehicle in the assembly shop. A T1 truck and a C1 car yield profits of $300 and $220, respectively, per vehicle sold. The aim of the objective function for Green Vehicle Inc. should be to Maximize the objective value. Part 2 The optimum solution is: Number of trucks to be produced per day = ? enter your response here
allons of deionized water from each wholesaler to each distribution center is shown in the following table: Question Viewer a. Which of the following statements regarding setting up the tableau for the optimal solution for this problem is true? B. The sum of supply capacities is greater than the sum of demands, so a dummy distribution center is needed. C. The sum of supply capacities is less than the sum of demands, so a dummy wholesaler is needed. b. What is the total cost of the solution? The optimal cost is $ ((Enter your response rounded to the nearest dollar.)
1. University Ceramics manufactures plates, mugs, and steins that include the campus name and logo for sale in campus bookstores. The time required for each item to go through the two stages of production (molding and finishing), the material required (clay), and the corresponding unit profits are given in the following table, along with the amount of each resource available for tomorrow's eight-hour shift. Available Plates Mugs Steins Molding (minutes) Finishing (minutes) 4 6 3 2,400 8 14 12 7,200 Clay (ounces) 5 4 3 3,000 Unit Profit $3.10 $4.75 $4.00 A linear programming model has been formulated in a spreadsheet to determine the production levels that would maximize profit. The solved spreadsheet model and corresponding sensitivity report are shown below. A 1 B C D E F G Plates 2 3 Unit Profit $3.10 Mugs $4.75 Steins $4.00 4 Resource Required per Unit Used Available 5 Molding (minutes) 3 2,400 <= 2.400 6 Finishing (minutes) 8 14 12 7.200 <<= 7.200 7 Clay (ounces) 5 4 3 2,700 <=…
The Ace Manufacturing Company has orders for three similar products. Product A Min B C 1 2 Machine 3 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. A A B B Ic C Product 1 12 3 Orders (units) 1,900 500 1,100 Capacity (units) 1,300 1,600 800 1 Machine 2 3 $1.00 $1.30 $1.10 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20 (a) Develop the linear programming formulation of this problem. (Let XA1 be the number of units of product A produced by machine 1, X;; be the number of units of product i produced by machine j, etc.)
(Linear Objective Function and Optimization Application) On a special occasion, renowned electronic giant retailer Best Buy sold a variety of TVs at a discounted prices or on huge sales. Task-1: Write down an appropriate equation for the net profit function, P in order to account for the net profit made by Best Buy after selling: (i) x-number of televisions (TVs) that made $250 profit on the sale of each SONY TVs (ii) y-number of televisions that made $10,500 profit on the sale of each PHILIP TVs respectively, in that event. Task-2: Profit margin, P as discussed in Task-1 was subject to the following constraints applied to the products. a. Maximum cost price was $5000 to manufacture each piece of SONY TVs and $10,000 to manufacture each piece of PHILIP TVs respectively. All TVs were manufactured at a maximum cost of $10 x106 as given in Plot No 1: Plot No. 1: ($5000 x + $ 10000y) ≤ $10 million; Graph the Plot No. 1 up to the scale in a paper. b. 10 and 150 employees worked to…
Chalimbana university farm is about to hire workers for its production of cabbage in a space of 5 months. as a student of farm management, you decide to increase the labour by 2 units at the first output,1 unit in the second and third output, 16 units in the fourth output and 20 units in the fifth output at each production level. The farm then realizes an output of 10,25, 65,30, and 30 in that period. The farm workers got a wage of k40 per month.a. Calculate the following at different level of output.i. marginal product, (MP) ii marginal revenue product (MRP) iii marginal resource cost (MRC)
Exercise 4 a) Write the objective function of this LP.b) Write the constraint of the basic element Y.c) Write the constraint that expresses"the factional contributions from each mine must add up to 1."d) What is the optimal fraction of a ton to be chosen from mine 4?e) To make the optimal fraction of a ton to be chosen from mine 4 non-zero, how should the cost per ton of ore from mine 4 change?f) If the minimum requirement amounts of basic element X increases to 7 tons, how much does the cost of a feasible blend (i.e., the value of the objective function) become?g) If the minimum requirement amount of basic element Z decreases to 25 tons, how much does the cost of a feasible blend (i.e., the value of the objective function) become?

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a. Formulate the problem of deciding how much of each product to make in the current week as a linear program. b. Solve this linear program graphically.