A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm’s goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 15x1 + 15x2 + 15x3+ 30x4 s.t. 7x1 + 13x2 + 11x3 + 10x4 ≤ 20 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x1 + x2 ≤ 1 {Constraint 3} x1 + x3 ≥ 1 {Constraint 4} x2 = x4 {Constraint 5} xj = 1, if location j is selected0, otherwise Solve this problem to optimality and answer the following questions: Which of the warehouse locations will/will not be selected?

A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm’s goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 15x1 + 15x2 + 15x3+ 30x4 s.t. 7x1 + 13x2 + 11x3 + 10x4 ≤ 20 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x1 + x2 ≤ 1 {Constraint 3} x1 + x3 ≥ 1 {Constraint 4} x2 = x4 {Constraint 5} xj = 1, if location j is selected0, otherwise Solve this problem to optimality and answer the following questions: Which of the warehouse locations will/will not be selected?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section6.3: Capital Budgeting Models

Problem 3P: Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows:...

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Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)
A Quezon-city based medium-sized firm has prepared the following binary integer program to evaluate a number of potential new capital projects. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 100x1 + 120x2 + 90x3 + 135x4 s.t. 150x1 + 200x2 + 225x3 + 175x4 ≤ 500 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x2 + x4 ≤ 1 {Constraint 3} x2 + x3 ≥ 1 {Constraint 4} x1 = x4 {Constraint 5} What is the expected net present value of the optimal solution? Group of answer choices
A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm’s goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 15x1 + 25x2 + 15x3+ 35x4s.t. 8x1 + 11x2 + 6x3 + 6x4 ≤ 17 {Constraint 1}x1 + x2 + x3 + x4 ≥ 2 {Constraint 2}x1 + x2 ≤ 1 {Constraint 3}x1 + x3 ≥ 1 {Constraint 4}x2 = x4 {Constraint 5} xj = {1, if location j is selected0, otherwisexj = 1, if location j is selected0, otherwise Solve this problem to optimality and answer the following questions: Which of the warehouse locations will/will not be selected? What is the net present value of the optimal solution? (Round your answer to the nearest whole number.) How much of the available capital will be spent (Hint: Constraint 1 enforces the available capital limit)? (Round your answer to the nearest whole number.)
A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm’s goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 15x1 + 25x2 + 15x3+ 35x4s.t. 8x1 + 11x2 + 6x3 + 6x4 ≤ 17 {Constraint 1}x1 + x2 + x3 + x4 ≥ 2 {Constraint 2}x1 + x2 ≤ 1 {Constraint 3}x1 + x3 ≥ 1 {Constraint 4}x2 = x4 {Constraint 5} xj = 0, 1 Solve this problem to optimality and answer the following questions: Which of the warehouse locations will/will not be selected? Location 1 will Answer Location 2 will Answer Location 3 will Answer Location 4 will Answer What is the net present value of the optimal solution? (Round your answer to the nearest whole number.) Net present value Answer How much of the available capital will be spent (Hint: Constraint 1 enforces the available capital limit)? (Round your answer to the nearest whole number.) Available capital Answer
A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm’s goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 30x1 + 30x2 + 25x3+ 20x4s.t. 5x1 + 10x2 + 8x3 + 12x4 ≤ 22 {Constraint 1}x1 + x2 + x3 + x4 ≥ 2 {Constraint 2}x1 + x2 ≤ 1 {Constraint 3}x1 + x3 ≥ 1 {Constraint 4}x2 = x4 {Constraint 5} xj = {1, if location j is selected0, otherwise xj = 1, if location j is selected0, otherwise Solve this problem to optimality and answer the following questions: Which of the warehouse locations will/will not be selected? What is the net present value of the optimal solution? (Round your answer to the nearest whole number.) How much of the available capital will be spent (Hint: Constraint 1 enforces the available capital limit)? (Round your answer to the nearest whole number.)
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A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm’s goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 35x1 + 25x2 + 15x3+ 30x4s.t. 7x1 + 8x2 + 7x3 + 13x4 ≤ 18 {Constraint 1}x1 + x2 + x3 + x4 ≥ 2 {Constraint 2}x1 + x2 ≤ 1 {Constraint 3}x1 + x3 ≥ 1 {Constraint 4}x2 = x4 {Constraint 5} xj = {1, if location j is selected0, otherwisexj = 1, if location j is selected0, otherwise Solve this problem to optimality and answer the following questions:
Hoosier Power needs to determine a capacity expansion plan to meet Bloomington’s power needs for the next 20 years. The current capacity is 5000 kwh. The demand for the current year is 4000 kwh, and demand is expected to increase by 1000 kwh in each succeeding year. At the beginning of each year, Hoosier Power must determine the amount of capacity to add, given the following inputs: ■ Any year in which capacity is added, a fixed cost of $120,000 is incurred plus a cost of $120 per kwh of capacity. ■ At most 10,000 kwh of capacity can be added in a single year. ■ It costs $25 per year to maintain a unit of capacity. ■ It costs $12 per year to produce a kwh. ■ If production does not meet demand, a shortage cost of $80 per kwh short is incurred. Develop a linear integer model to help Hoosier Power minimize its costs for the next 20 years.
A company imports goods at two ports: Philadelphia and New Orleans. Shipments of one product are made to customers in Atlanta, Dallas, Columbus, and Boston. For the next planning period, the supplies at each port, customer demands, and shipping costs per case from each port to each customer are as follows: Customers Port Atlanta Dallas Columbus Boston Port Supply Philadelphia 2 6 6 2 5,000 New Orleans 1 2 5 7 3,000 Demand 1,400 3,200 2,000 1,400 Develop a network representation of the distribution system. Develop the objective function and the constraints.
Formulate a system of equations for the situation below and solve.Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units and two- and three-bedroom townhouses. A total of 204 units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom units, find how many units of each type will be in the complex. one-bedroom units units two-bedroom townhouses units three-bedroom townhouses units
Given this linear programming model, solve the model and then answer the questions that follow. Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc. Subject to Machine: 5x 1 + 4x 2 + 3x 3 ≤ 160 minutes Labor: 4x1 + 10x2 + 4x3 ≤ 288 hours Materials: 2x 1 + 2x2 + 4x3 ≤ 200 pounds Product 2: x2 ≤ 16 units x1, x2, x3 ≥ 0 a) Are any constraints binding? If so, which one(s)? b) If the profit on product 3 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. c) If the profit on product 1 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. d) If 10 hours less of labor time were available, what would the values of the decision variables be? The objective function? Explain. e) If the manager decided that as many as 20 units of product 2 could be produced (instead of 16), how much additional profit would be generated? f) If profit per unit on each…
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?