B.4. Consider the following linear programming problem:
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- 13-4 see picture to solvearrow_forwardL.P. Model: Maximize Subject to: Z= 1X + 10Y 4X + 3Y ≤ 36 2X+4Y ≤ 40 1Y27 X,Y 20 (C₁) (C₂) (C3) 1.) Plot and label the constraints C₁, C₂ and C3 (using the line drawing tool) on the provided graph. 2.) Using the point drawing tool, plot the point that maximizes the objective function. The optimum solution is: X = (round your response to two decimal places). Y = (round your response to two decimal places). Optimal solution value Z = (round your response to two decimal places). C Y 22- 20- 18- 16- 14- 12- 10- 8- co 6+ 4- 2- ó -~ 0 2 -4 4 -6 8 10 12 X . . 14 16 18 20 22 Lyarrow_forwardshort answerarrow_forward
- Problem 3-19 (Algorithmic) Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit are as follows: Category Profit/unit Machine 1 time/unit Machine 2 time/unit Product 1 2 3 Two operators are required for machine 1; thus, 2 hours of labor must be scheduled for each hour of machine 1 time. Only one operator is required for machine 2. A maximum of 90 labor-hours is available for assignment to the machines during the coming week. Other production requirements are that product 1 cannot account for more than 50% of the units produced and that product 3 must account for at least 10% of the units produced. a. How many units of each product should be produced to maximize the total profit contribution? If required, round your answers the nearest whole number. If your answer is zero, enter "0". Profit = $ $ Machine 2 What is the projected weekly profit associated…arrow_forwardProblem 6-09 (Algorithmic) The Ace Manufacturing Company has orders for three similar products: Product Order (Units) A 1750 B 500 C 1100 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 as follows: Machine Capacity (Units) 1 1550 2 1450 3 1150 Product Machine A B C 1 $0.80 $1.30 $0.70 2 $1.40 $1.30 $1.50 3 $0.80 $0.80 $1.20 Use the transportation model to develop the minimum cost production schedule for the products and machines. Show the linear programming formulation. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". The linear programming formulation and optimal solution are shown. Let xij = Units of…arrow_forwardProblem 3. Let P2 be the vector space of polynomials of degree 2 equipped with the inner product >= † p(x)}q(x) dr. S = Let W be a subspace of P2 generated by the polynomial x 1. Find an orthogonal basis of the orthogonal complement of W.arrow_forward
- Problem 10-21 (Algorithmic) United Express Service (UES) uses large quantities of packaging materials at its four distribution hubs. After screening potential suppliers, UES identified six vendors that can provide packaging materials that will satisfy its quality standards. UES asked each of the six vendors to submit bids to satisfy annual demand at each of its four distribution hubs over the next year. The following table lists the bids received (in thousands of dollars). UES wants to ensure that each of the distribution hubs is serviced by a different vendor. Which bids should UES accept, and which vendors should UES select to supply each distribution hub? Distribution Hub Bidder 1 2 3 4 Martin Products 190 165 120 240 Schmidt Materials 140 240 150 200 Miller Containers 215 210 145 235 D&J Burns 175 185 190 290 Larbes Furnishings 200 185 155 230 Lawler Depot 230 190 140 230 Bidder Decision Bid Martin Products Schmidt Materials Miller…arrow_forwardProblem 4-11 (Algorithmic) Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows: Supplier Component 1 2 3 1 $11 $12 $13 2 $9 $10 $9 Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows: Supplier 1 2 3 Capacity 500 900 700 If the Edwards production plan for the next period includes 900 units of component 1 and 700 units of component 2, what purchases do you recommend? That is, how many units of each…arrow_forwardexample 1a 1.plot all the corner points for the feasible area. 2. Find the optimum solution to X= Y= VALUE Z=arrow_forward
- 3. The Captain of a Cricket team has to allot 5 middle position to 5 batsmen. The average runs scored by each batsman at these positions are as follows Batting Positions III Batsmen II IV V P 40 40 35 25 50 27 50 42 30 16 25 R. 50 48 40 60 20 19 20 18 25 T 58 60 59 55 Find the assignment of batsmen to positions, which would give the maximum number of runs. If another batsman 'U' with the following average runs in batting positions as given below: Batting Positions: Average Runs: Is added to the team, should he be added to play in the team? If so, who should be replaced by him? II II IV V 45 52 38 50 49arrow_forwardQ1. A manufacturing firm has discontinued production of a certain unprofitable product line. This created considerable excess production capacity. Management is considering to devote this excess capacity to one or more of three product 1,2 and 3. The available capacity on the machines which might limit output are given below: Machine type Milling machine Lathe Grinder Available time (in machine hours per week) 250 Milling Lathe Grinder 150 50 The number of machine hours required for each units of the respective product is given below; Machine type Productivity (in machine hours/unit) Product 1 Product 2 8 4 2 2 3 0 Product 3 3 0 1 The unit profit would be 20 birr, 6 birr and 8 birr for products 1,2 and 3. Find how much of each product the firm should produce in order to maximise profit ? Solve the problem by simplex method.arrow_forwardTheme Park (5S-7A) The lease of Theme Park, Inc., is about to expire. Management must decide whether to Renew the lease for another 10 years or to Relocate near the site of a proposed new motel. The town planning board is currently debating the merits of granting approval to the motel. A consultant has estimated the net present value of Theme Park's two alternatives under each state of nature as shown below. Suppose that the management of Theme Park, Inc., has decided that there is a 0.20 probability that the motel's application will be approved. Options Renew Relocate Alternative Renew Relocate Motel Approved a-1. If management uses maximum expected monetary value as the decision criterion, calculate expected monetary value for the alternatives "Renew" and "Relocate"! $ 400,000 2,000,000 O Renew O Relocate Motel Rejected $4,000,000 100,000 Expected Value a-2. Which alternative should it choose? b. If management has been offered the option of a temporary lease while the town planning…arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,