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A strawberry growing company is deciding its production and sale plan for the national and international markets.
The sale price for each ton of strawberry depends on the quantity offered in the market. If x1 tons is offered for the domestic market, the sale price will be (30 - x1) CU / ton, while if x2 tons is offered for the international market, the sale price will be (40 - x2) CU / ton.
The cost for each ton of strawberry for the domestic market is 10 MUs, while for the international market it is 15 MUs.
The company has the capacity to produce up to 10 tons of strawberries for sale and, according to SAG restrictions, it must dedicate at least 10% of its production to the international market.
For technical production reasons, the company must additionally satisfy the following restriction: x12 + x22 ≤64.
a) Raise the NLP model that allows maximizing the net profit for the company
b) State the KKT conditions for the problem and indicate whether they are necessary and / or sufficient.
c) Analyze all the points that could satisfy the KKT conditions and determine the optimal solution of the problem. Describe graphically what happens in each case.
d) There is the option of buying new machinery to increase the production capacity of the company. In what range should the new machine increase production capacity to suit the company? How much would you be willing to pay for it?
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- A strawberry growing company is deciding its production and sale plan for the national and international markets.The sale price for each ton of strawberry depends on the quantity offered in the market. If x1 tons is offered for the domestic market, the sale price will be (30 - x1) CU / ton, while if x2 tons is offered for the international market, the sale price will be (40 - x2) CU / ton.The cost for each ton of strawberry for the domestic market is 10 MU, while for the international market it is 15 MU.The company has the capacity to produce up to 10 tons of strawberries for sale and according to SAG restrictions, it must dedicate at least 10% of production to the international market.For technical production reasons, the company must additionally satisfy the following restriction: x12 + x22 ≤64.d) There is the option of buying new machinery to increase the production capacity of the company. In what range should the new machine increase production capacity to suit the company? How…A factory manager is planning for the manufacture of plywood to be sold overseas. The fixed cost of operation is estimated at $800,000 per month while the variable cost is $155 per thousand board feet of plywood. The selling price will depend on how much will be produced and sold and is determined by the relationship, price per thousand board feet, p = $600 – 0.05D, where D is the amount produced and sold in thousands of board feet. Determine the range of profitable production. For profitable production, production must be at least thousands of board feet per month, but not more than (Round to the nearest unit.)Rail Tours, Inc., sells packaged tours on rail lines, including gourmet meals and a reserved bed. The most popular tours are in the autumn, when foliage colors are at their peak. The overnight package for Saturday and Sunday morning are especially heavily booked. A market survey firm has just completed a study in which they conclude that if the package cost is $200 per couple, then Rail Tours can expect to sell 400 spaces on a typical Saturday. If the price is raised to $225, then unit sales will drop to 390. If the price is raised further to $250, unit sales drop to 380. a) From the data given, write down the demand equation and determine its intercepts. Are there any precautions needed when operating at the extreme ends of the demand curve?b) The survey firm also reports that if per capita income changes, Rail Tours can expect a large change in bookings. In particular, if per capita income falls by 1%, then bookings will tend to fall by about 2%. Are tour packages a normal good?…
- A factory manager is planning for the manufacture of plywood to be sold overseas. The fixed cost of operation is estimated at $800,000 per month while the variable cost is $155 per thousand board feet of plywood. The selling price will depend on how much will be produced and sold and is determined by the relationship, price per thousand board feet, p = $600 – 0.05D, where D is the amount produced and sold in thousands of board feet. Determine the monthly production that will maximize the total profit and corresponsding price. Dettermine also the corresponding maximum profit per month. A) For maximum profit, (to the nearest unit) thousands of board feet per month must be produced and sold at per thousand board feet of plywood.(Round to the nearest cent.) B) The maximum profit per month is equal to $A local company assembling stereo radio cassette produces 300 units per month at a cost of ₱700 per unit. Each stereo radio cassette sells for ₱1,200. If the firm makes a profit of 10% on its 10,000 shares with a par value of ₱200 per share and the total cost per month is ₱20,000. How many units gives the break-even point and how much is the loss or profit if only 100 units are produced in a given month?Soft selling occurs when a buyer is skeptical of the usefulness of a product and the seller offers to set a price that depends on realized value. For example, suppose a sales representative is trying to sell a company a new accounting system that will, with certainty, reduce costs by 10%. However, the customer has heard this claim before and believes there is only a 40% chance of actually realizing that cost reduction and a 60% chance of realizing no cost reduction. Assume the customer has an initial total cost of $400. According to the customer's beliefs, the expected value of the accounting system, or the expected reduction in cost, is . Suppose the sales representative initially offers the accounting system to the customer for a price of $28.00. The information asymmetry stems from the fact that the has more information about the efficacy of the accounting system than does the . At this price, the customer purchase the accounting system, since the expected…
- Your company is contemplating bidding on an RFP (Request For Proposal) to produce 100,000 units of a specialized part. Suppose, however, that the requesting company really needs only 90,000 units of the part. Also assume that, because the part is specialized, potential suppliers do not yet possess the machines and factories needed to produce it and that overhead expenses involved in production have yet to be incurred. Suppose the average costs of all potential suppliers are as follows: Units Average Total Cost (Dollars Per Unit) 90,000 4 100,000 3 True or False: The requesting company can solicit lower bids by requesting 100,000 units as opposed to 90,000.Soft selling occurs when a buyer is skeptical of the usefulness of a product and the seller offers to set a price that depends on realized value. For example, suppose a sales representative is trying to sell a company a new accounting system that will, with certainty, reduce costs by 20%. However, the customer has heard this claim before and believes there is only a 40% chance of actually realizing that cost reduction and a 60% chance of realizing no cost reduction. Assume the customer has an initial total cost of $600. According to the customer's beliefs, the expected value of the accounting system, or the expected reduction in cost, is ____ . Suppose the sales representative initially offers the accounting system to the customer for a price of $84.00. The information asymmetry stems from the fact that the Customer/Sales Rep has less information about the efficacy of the accounting system than does the Customer/Sales Rep . At this price, the customer will/will not…The Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requires 3 hours to assemble and 12 hour to paint, and the economy model requires 2 hours to assemble and 1 hour to paint. The maximum number of assembly hours available is 24 per day, and the maximum number of painting hours available is 8 per day. If the profit on the deluxe model is $92 per unit and the profit on the economy model is $74 per unit, how many units of each model will maximize profit?
- Soft selling occurs when a buyer is skeptical of the usefulness of a product and the seller offers to set a price that depends on realized value. For example, suppose a sales representative is trying to sell a company a new accounting system that will, with certainty, reduce costs by 10%. However, the customer has heard this claim before and believes there is only a 20% chance of actually realizing that cost reduction and a 80% chance of realizing no cost reduction. Assume the customer has an initial total cost of $200. According to the customer's beliefs, the expected value of the accounting system, or the expected reduction in cost, is $____ . Suppose the sales representative initially offers the accounting system to the customer for a price of $12.00. The information asymmetry stems from the fact that the ______(sales rep or buyer) has less information about the efficacy of the accounting system than does the ______(sales rep or buyer) . At this price, the…ABC Company has the following information: Variable Cost per Unit is P 15; Fixed Expenses is P54,000; and Selling Price per Unit is P20. What should be the selling price per unit if break-even point is brought down to 6,000 units? ABC Company has the following information: Variable Cost per Unit is P 15; Fixed Expenses is P54,000; and Selling Price per Unit is P20. If the company will only sell 10,000 units for the month, how much profit or loss will they get?At an output of 14, MC = $50 and ATC = $55. At an output of 15, MC = $65 and ATC= $56. Estimate the ATC at the break-even point