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+ 15x4 s.t. 4x1 + 12x2 + 6x3 +7x4 $ 16 (Constraint 1) x1+ x2 + x3 +x4 2 2 (Constraint 2) x1 + x2 s 1 (Constraint 3) x1+ x3 2 1{Constraint 4) x2 = x4 (Constraint 5) [ 1, if location jis selected 0, otherwise エj = Solve this problem to optimality and answer the following questions: a. Which of the warehouse locations will/will not be selected? Location 1 will Location 2 will Location 3 will Location 4 will
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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 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+ 30x4s.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 + 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 AnswerA 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.)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:
- 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 choicesAn individual wishes to invest PhP 50,000 over the next year in two types of investment: Investment A yields 5%, and investment B yields 8%. Market research recommends an allocation of at least 25% of the actual total investment in A and at most 50% of the actual total investment in B. Moreover, investment in A should be at least half the investment in B. How should the fund be allocated to the two investments? questions: -Find the feasible region -Find the corner points -Find the optimal valueFormulate 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
- A decision problem has the following three constraints: 70X + 6Y <= 420; 24X + 3Y= 72; and 11X - Y <= 14 . The objective function is Min 17X + 38Y . The objective function value is : a. 338 b. 676 c. unbounded d. infeasible e. 0formulate a linear program Vince Oliver plans to invest P 30,000 in municipal bonds, savings bonds, and treasury bills. He wishes to invest a minimum of P 5,000 in each of the three. If the interest rates are 12% for municipal bonds, 8% for savings bonds, and 10% for treasury bills, how much should he invest in each?The management of Sunny Skies Unlimited now has decided that the decision regarding the locations of the paramedic stations should be based mainly on costs. The cost of locating a paramedic station in a tract is $200,000 for tract 1, $250,000 for tract 2, $400,000 for tract 3, $300,000 for tract 4, and $500,000 for tract 5. Management’s objective now is to determine which tracts should receive a station to minimize the total cost of stations while ensuring that each tract has at least one station close enough to respond to a medical emergency in no more than 15 minutes. In contrast to the origi- nal problem, note that the total number of paramedic stations is no longer fixed. Furthermore, if a tract without a station has more than one station within 15 minutes, it is no longer neces- sary to assign this tract to just one of these stations. Display and solve this model on a spreadsheet.