B.4. Consider the following linear programming problem:
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- 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_forwardThe Bayside Art Gallery is considering installing a video camera security system to reduce its insurance premiums. A diagram of the eight display rooms that Bayside uses for exhibitions is shown in the figure below; the openings between the rooms are numbered 1 through 13. Entrance Room 1 Room 2 1 4 8 12 Room 3 Room 4 7 Room 5 10 Room 6 2 5 13 Room 7 11 Room 8 A security firm proposed that two-way cameras be installed at some room openings. Each camera has the ability to monitor the two rooms between which the camera is located. For example, if a camera were located at opening number 4, rooms 1 and 4 would be covered; if a camera were located at opening 11, rooms 7 and 8 would be covered; and so on. Management decided not to locate a camera system at the entrance to the display rooms. The objective is to provide security coverage for all eight rooms using the minimum number of two-way cameras.arrow_forwardMaximize p = 10x + 20y + 15z subject to x + 2y + z ≤ 40 2y − z ≥ 10 2x − y + z ≥ 20 x ≥ 0, y ≥ 0, z ≥ 0.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 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_forwardL.P. Model: Minimize Subject to: Z = 24X + 15Y 7X+11Y 288 16X+4Y≥64 X,Y 20 On the graph on right, constraints C, and C, have been drawn. Using the point drawing tool, plot all the corner points for the feasible area. (C₁) (C₂) 24- 22- 20- 18- 16- 14- 12- 104 8 6- 4- 2- 0+ 0 2 4 6 8 10 12 14 16 18 20 22 24 X Q Sarrow_forward
- Problem 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_forwardL.P. Model: Minimize Subject to: Z = 15X+12Y 7X+11Y288 (C₂) (C₂) 16X+4Y280 X,Y 20 On the graph on right, constraints, C, and C₂ have been drawn. Using the point drawing tool, plot all the corner points for the feasible area. 24- 22- 20- 18- 16- 14- 12- 10 8- 64 4- 2- -N 10 12 14 16 18 20 22 24 X C Garrow_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_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_forward3. Consider the following linear program: Min 8X + 12Y s.t. IX +3Y 9 2X+ 2Y 10 6X + 2Y 18 XY 0 Use the graphical solution procedure to find the optimal solution. b. Assume that the objective function coefficient for X changes from 8 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. a. Assume that the objective function coefficient for X remains 8, but the objective func- tion coefficient for Y changes from 12 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. d. The sensitivity report for the linear program in part (a) provides the following objec- tive coefficient range information: C. Objective Coefficient Allowable Inerease Allowable Variable Decrease 8.000 12.000 4.000 12.000 4.000 4.000 How would this objective coelficient range information help you answer parts (b) and (C) prior to resolving the problem?arrow_forwardLinear programming model formulation. Data Decision variables Objectives Constraintsarrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,