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Solve each of these problems by computer and obtain the optimal values of the decision variables and the objective function.
a.
b.
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Chapter 19 Solutions
OPERATIONS MANAGEMENT W/ CNCT+
- Solve these problems using graphical linear programming and answer the questions that follow. Usesimultaneous equations to determine the optimal values of the decision variables.a. Maximize Z = 4x1 + 3x2Subject toMaterial 6x1 + 4x2 ≤ 48 lbLabor 4x1 + 8x2 ≤ 80 hrx1, x2 ≥ 0 b. Maximize Z = 2x1 + 10x2Subject toDurability 10x1 + 4x2 ≥ 40 wkStrength 1x1 + 6x2 ≥ 24 psi Time 1x1 + 2x2 ≤ 14 hrx1, x2 ≥ 0 c. Maximize Z = 6A + 3B (revenue)Subject toMaterial 20A+ 6B ≤ 600 lbMachinery 25A+ 20B ≤ 1,000 hr Labor 20A+ 30B ≤ 1,200 hrA, B ≥ 0 (1) What are the optimal values of the decision variables and Z?arrow_forwardSolve each of these problems by computer and obtain the optimal values of the decision variables and the objective function. Maximize Z = 4x1 + 2x2 + 5x3 Subject to 1x1 + 2x2 + 1x3 ≤ 25 1x1 + 4x2 + 2x3 ≤ 40 3x1 + 3x2 + 1x3 ≤ 30 x1, x2, x3 ≥ 0 Maximize Z = 10x1 + 6x2 + 3x3 Subject to 1x1 + 1x2 + 2x3 ≤ 25 2x1 + 1x2 + 4x3 ≤ 40 1x1 + 2x2 + 3x3 ≤ 40 x1, x2, x3 ≥ 0arrow_forwardWhat combination of x and y will yield the optimum for this problem? Maximize $10x + $4y, subject to (1) 5x + 3y ≤ 15 and (2) 3x + 6y ≤ 18 and (3) x, y ≥ 0.arrow_forward
- Photo attached. A decision tree in excel has to be used to solve this problem.arrow_forwardAl, Barbara, Carol, and Dave have joined together to purchase two season tickets to the Giants’ home football games. Because there are eight home games, each person will get tickets to two games. Each person has ranked the games they prefer from 1 to 8, with 1 being most preferred and 8 least preferred, as follows: Determine the two games each person should get tickets for that will result in the groups’ greatest degree of satisfaction. Do you think the participants will think your allocation is fair?arrow_forwardThe High-Price Oil Company owns a pipeline network that is used to convey oil from its source to several storage locations. A portion of the network is as follows: Due to the varying pipe sizes, the flow capacities vary. By selectively opening and closing sections of the pipeline network, the firm can supply any of the storage locations. a. If the firm wants to fully utilize the system capacity to supply storage location 7, how long will it take to satisfy a location 7 demand of 100,000 gallons? What is the maximal flow for this pipeline system? b. If a break occurs on line 2–3 and that line is closed down, what is the maximal flow for the system? How long will it take to transmit 100,000 gallons to location 7?arrow_forward
- Find the indicated maximum or minimum value of the objective function in the linear programming problem. Minimize g = 10x + 6y subject to the following. x + 2y ≥ 10 2x + y ≥ 11 x + y ≥ 9 x ≥ 0, y ≥ 0arrow_forwardConsider the following linear programming problem: Min Z = 50x1 + 60x2 s.t. 6x1 + 5x2 >= 30 8x1+4x2 >= 32 x1,x2 >=0. What is the Z in the optimal point of this problem? a. 200 b. 250 c. 300 d. 350 e. none of the abovarrow_forwardConsider the following LP problem: Min 6X+ 18Y; Subject to : 3 X + 9Y <= 47, and X + Y <= 141. Which one of the following is true?: a. Slack for each constraint is zero. b. Optimal Obj. function value is 94 c. X=70.5, Y=70.5 is the only optimal solution. d. Optimal Obj. function value is 0arrow_forward
- In the problem on excel : 1.What are the decision variables 2.What is the objective functions 3. What are the 11 constraints and explain A used t company, owned by Musa in Ottawa sells 7 different brands covering 3 different products. These are 4 Brands of Cars: Toyota, Honda, Chevrolet and BMW; 2 brands of Motorcycles: Suzuki and Yamaha, and 1 brand of Sailboats: Amel. Musa knows that his sales floor which he will display his products is 70,000 square feet, and that a Car takes 60 square feet of space, a motorcycle takes 20 square feet of space, and a sailboat takes 800 square feet of space. The profit that can be made for selling each of 7 different items is listed below: ITem Profit per unit Car - Toyota $2800 Car - Honda $3900 Car - Chevrolet $2,100 Car - BMW $5000 Motorcycle - Suzuki $1,000 Motorcycle - Yamaha $2,250 Sailboat - Amel $9,500 The transportation company is trying to determine how many of each item to order to maximize profit, given the following restrictions:…arrow_forwardFind the optimal solution for the following problem. (Round your answers to 3 decimal places.) Maximize C = 13x + 3y subject to 12x + 14y ≤ 21 15x + 20y ≤ 37 and x ≥ 0, y ≥ 0. What is the optimal value of x?arrow_forwardSolve this using the hungarian model and also write the decision variable and the constraints.arrow_forward
Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,