The AC company decides to open a new factory to satisfy increasing demand. They already have four plants, (A, B, C and D) and want to open a new one in site E or F. 4 B C D Factory Wharehouse W1 W2 W3 The capacity of the new plant is going to be 40.000 units The company distributes to the following wharehouses: Expected Annual Demand Capacity A 3 C D E = 20,000 50,000 35,000 70,000 80,000 50,000 70,000 The Logistics department compiled the following cost table specifying the cost per unit to ship the product from each plant to each warehouse: Plant Warehouse W2 2 4 4 1 2 3 W1 1 1 2 5 1 5 Evaluate wich site E or F is more convenient. W3 2 1 5 2 3 4
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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 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 Answer
- 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 the objective function and the constraints.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.)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:
- Please do not give solution in image formate thanku. Hoosier Power needs to determine a capacity expansion plan to meet Bloomington’s power needs for the next 20 years. The current capacity is 5,000 kWh. The demand for the current year is 4,000 kWh, and demand is expected to increase by 1,000 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 $24 per year to maintain a unit of capacity; It costs $12 per year to produce one kWh; If production does not meet demand, a shortage cost of $75 per kWh short is incurred. Hoosier Power wants to determine a capacity expansion plan with the minimal total cost to meet Bloomington’s power needs for the next 20 years. Define the decision variables and write down the…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.The Acme Company operates four factories that ship products to five warehouses. The shipping costs, requirements capacities, and optimal allocations are shown below. Factory Shipping Cost per Case to Warehouses Capacity W1 W2 W3 W4 W5 F1 $1.50 $4.50 $6.00 $7.50 $9.00 40,000 30,000 10,000 F2 $3.00 $3.00 $1.50 $6.00 $7.50 30,000 25,000 5,000 F3 $1.50 $7.50 $1.50 $4.50 $1.50 30,000 10,000 20,000 F4 $7.50 $3.00 $6.00 $7.50 $6.00 25,000 25,000 Demand 30,000 35,000 25,000 15,000 20,000 125,000 What is the total cost of the optimal solution? Total cost = $nothing. (Enter your response to the nearest dollar.)
- Al, 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?The Gulf Coast Foundry is developing a long-range strategic plan for buying scrap metal for its foundry operations. The foundry can buy scrap metal in unlimited quantities from two sources, Atlanta (A) and Birmingham (B), and it receives the scrap daily in railroad cars. The scrap is melted down, and lead and copper are extracted for use in the foundry processes. Each railroad car of scrap from source A yields 1 ton of copper and 1 ton of lead and costs $10,000. Each railroad car of scrap from source B yields 1 ton of copper and 2 tons of lead and costs $15,000. If the foundry needs at least 21/2 tons of copper and at least 4 tons of lead per day for the foreseeable future, how many railroad cars of scrap should be purchased per day from Source A and Source B to minimize the long-range scrap metal cost?Rand Enterprises is considering a number of investment possibilities. Specifically, each investment under consideration will draw on the capital account during each of its first three years, but in the long run, each is predicted to achieve a positive net present value (NPV). Listed here are the investment alternatives, their net present values, and their capital requirements, and all figures are in millions of dollars. In addition, the amount of capital available to the investments in each of the next three years is predicted to be $20 million, $12 million, and $20 million, respectively. Project One-PhaseExpansion Two-PhaseExpansion TestMarket AdvertisingCampaign BasicResearch PurchaseEquipment NPV 5.0 8.1 11.6 5.3 10.4 4.2 Year 1 Capital 3.6 3.0 7.2 2.4 6.0 1.2 Year 2 Capital 1.2 4.2 4.8 1.8 1.2 0.6 Year 3 Capital 4.8 4.2 6.0 2.2 4.8 1.1 In addition, the following constraints have to be met: a. The expansion investments are mutually exclusive and only one of…