Formulate as a constrained nonlinear program. Clearly indicate the variables, objective function, and constraints.
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An engineer at Fertilizer Company has synthesized a sensational new fertilizer made of just two interchangeable basic raw materials. The company wants to take advantage of this opportunity and produce as much as possible of the new fertilizer. The company currently has $40,000 to buy raw materials at a unit price of $8000 and $5000 per unit, respectively. When amounts x1 and x2 of the basic raw materials are combined, a quantity q of fertilizer results given by: q = 4x1 + 2x2 - 0.5x12 - 0.25x22
Part A: Formulate as a constrained nonlinear program. Clearly indicate the variables, objective function, and constraints.
Part B: Solve the Program with Excel Solver (provide exact values for all variables and the optimal objective function).
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- A manufacturer has a production facility that requires 15,604 units of component JY21 per year. Following a long-term contract, the manufacturer purchases component JY21 from a supplier with a lead time of 7 days. The unit purchase cost is $25.6 per unit. The cost to place and process an order from the supplier is $121 per order. The unit inventory carrying cost per year is 10.5 percent of the unit purchase cost. The manufacturer operates 250 days a year. Assume EOQ model is appropriate. If the manufacturer uses a constant order quantity of 2,640 units per order, what is the annual holding cost? Use at least 4 decimal places.A firm produces three products. Product A sells for $60; its variable costs are $20. Product B sells for $200; its variable costs are $120. Product C sells for $25; its variable costs are $10. Last year, the firm sold 1000 units of A 2000 units of B, and 10,000 units of C The firm has fixed costs of $320,000 per year. Calculate the break-even point of the firm.The GIIC -Company must determine a policy for ordering coal to operate 15 smelters. Each smelter requires exactly 5 tons of coal per day to operate, and the firm operates 360 days per year. The purchasing manager has negotiated a contract to obtain the coal for 5 BD per ton for the coming year. The purchasing manager has determined that the ordering cost is 40 BD per order, and the cost of holding coal is 20% per ton of its value. i. Determine the optimal quantity of coal to receive in each order. ii. Determine the total inventory-related costs associated with the optimal ordering policy (do not include the cost ii. If five days' lead time is required to receive an order of coal, how much coal should be on hand when an iv. Optimal quantity 1837.11 Tons, Total cost 1837.11 BD, Inventory during LT 275 Tons of the coal). order is placed? i. Optimal quantity 1469.694 Tons, Total cost 1469.694 BD, Inventory during LT 375 Tons ii. Optimal quantity 734.85 Tons, Total cost 1649.694 BD,…
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- Neverland Company, a retailer, plans to sell 15,000 units of Product X during the month of August. If the company has 2,500 units on hand at the start of the month, and plans to have 2,000 units on hand at the end of the month, how many units of Product X must be purchased from the supplier during the month? * 17,000 15,000 14,500 15,500XYZ Corporation manufactures two products, Simple and Complex. The following annual information was gathered: Simple Complex Selling price per unit P47.00 P26.00 Variable cost per unit 42.00 22.00 Total annual fixed costs are P18,000. Assume XYZ Corporation can produce and sell any mix of Simple or Complex at full capacity. It takes one hour to make one unit of Complex. However, Simple takes 50% longer to manufacture when compared to Complex. Only 120,000 hours of plant capacity are available. How many units of Simple and Complex should XYZ Corporation produce and sell in a year to maximize profits?Joint Products Choi Company manufactures two skin care lotions, Smooth Skin and Silken Skin,from a joint process. The joint costs incurred are $420,000 for a standard production run that generates 180,000 pints of Smooth Skin and 120,000 pints of Silken Skin. Smooth Skin sells for $2.40 perpint, while Silken Skin sells for $3.90 per pint.Required1. Assuming that both products are sold at the split-off point, how much of the joint cost of each production run is allocated to Smooth Skin using the relative sales value method?2. If no separable costs are incurred after the split-off point, how much of the joint cost of each productionrun is allocated to Silken Skin using the physical measure method method?3. If separable processing costs beyond the split-off point are $1.40 per pint for Smooth Skin and $0.90 perpint for Silken Skin, how much of the joint cost of each production run is allocated to Silken Skin usinga net realizable value method?4. If separable processing costs beyond the…
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