To reduce shipping distances between the manufacturing facilities and a major consumer, a Korean computer brand, Intel Corp. intends to start production of a new controlling chip for Pentium III microprocessors at their two Asian plants. The cost of producing x1 chips at Chiangmai (Thailand) is C = 0.002x? + 4x1 + 500, and the cost of producing x2 chips at Kuala-Lumpur (Malaysia) is C2 = 0.005x3 + 4x2 + 275 . The Korean computer manufacturer buys them for RM150 per chip. b) i) Find the quantity that should be produced at each Asian location to maximize the profit. ii) Using the second order condition (SOC), prove that the profit is at the maximum.
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- A company produces two different versions of a certain product. Let q₁ indicate the amount produced of the first version. The cost function c(q₁) for the first version (expressed in euros) can be described by the equation c(q₁) = 9₁ · √√0.59² +59₁ 10 a) For which value(s) of q₁ is the instantaneous rate of change of the cost function equal to 1.75? You may use the graphical calculator to find zeros of a polynomial function if needed. b) Using the result from a), give a precise economic meaning for the instantaneous rate of change of 1.75. We now denote 92 as the amount produced of the second version. The equation of the cost function c(9₂) for the second version is unknown. We do know that the current cost for a production of 2 units of the second version is 50 monetary units and that the elasticity of the cost in terms of the produced amount when 92 = 2 is equal to 1.88. c) Give a linear approximation ƒ of the cost function c(9₂) for production amounts close to q₂ = 2.A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price=160−0.02×Demand for an annual printing of this particular product. The fixed costs per year (i.e., per printing)=$47,000 and the variable cost per unit=$40. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 4,000 units per year. The maximum profit that can be achieved is $? (Round to the nearest dollar.) The unit price at the point of optimal demand is $? per unit. A large wood products company is negotiating a contract to sell plywood overseas. The fixed cost that can be allocated to the production of plywood is $800,000 per month. The variable cost per thousand board feet is $155.50. The price charged will be determined by p=$600−(0.05)D per 1,000 board feet. a. For this situation, determine the optimal monthly sales volume for this product and calculate the profit (or loss) at the optimal volume. b. What is the domain of profitable demand during a month?
- 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 companyb) State the KKT conditions for the problem and indicate whether they are necessary and / or sufficient.c)…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…= 2. The cost of operating a jet-powered commercial (passenger- carrying) airplane varies as the three-halves (3/2) power of its velocity; specifically, Co kny3/2, where n is the trip length in miles, k is a constant of proportionality, and vis velocity in miles per hour. It is known that at 400 miles per hour, the average cost of operation is $300 per mile. The company that owns the aircraft wants to minimize the cost of operation, but that cost must be balanced against the cost of the passengers' time (CC), which has been set at $300,000 per hour. At what velocity should the trip be planned to minimize the total cost, which is the sum of the cost of operating the airplane and the cost of passengers' time?
- Intelligent Inc. specializes in the manufacture ofcomponents for personal computers. Managementhas determined that the daily cumulative cost of producing these components (in dollars) is given by:C(x) = 0.0001x3 - 0.08x2 + 40x + 5000where x is the number of components produced.(a) What is the actual cost incurred for manufacturing the 301st component?(b) What is the marginal cost of the 200th component? What can you say about the marginal costas a function of x (increasing or decreasing)?(c) What is the average unit cost if you produce just300 units?If company A manufactures t-shirts and sells them to retailers for US$9.80 each It has fixed costs of $2625 related to the production of the t-shirts, and the production cost per unit is US$2.30. Company B also manufactures t-shirts and sell them directly to consumers. The demand for its product is p = 15 − x/125 ,its production cost per unit is US$5.00 and its fixed cost are the same as for company A. Derive the total revenue function, R(x) for company. Derive the profit function, Π(x) for company. How many t-shirts must company B sell to in order to break-even? How many t-shirts must company B sell to maximize its profit?A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p = 77 – 0.12D units. The fixed cost is $800 per month and the variable cost $25 per unit produced. What number of units, D*,should be produced per month and sold to maximize the profit per month related to the product? Round your answer to 2 decimal places.
- A small business woman has realized that for one of her products, if the price per unit is GH¢20 she can sell 300 units a day. On the other hand, if the price per unit is reduced to GH¢13, she can sell 440 units a day. From the accounting records, her accountant has estimated the fixed cost of production as GH₵2,000 with a variable cost per unit of GH¢10. (i). Find an expression relating price and output assuming it is linear. (ii). State the total cost function, assuming it is linear. (iii) Advise the business woman on the level of production at which she will breakeven.Thranduil company's market research department is working on the pricing of a product. The field research shows that average demand is expected to be 8000 units at price 50 TL. From this point, each 1 TL change in price will negatively affect demand with a magnitude of 100 units. Fixed and variable costs are confronted for producing the product. According to the information obtained from the financial department, 200,000 TL is the estimate of fixed costsand 20 TL is the estimate of variable costs per unit produced. Assume that all units produced are sold. Which revenue equation (R(p)) is given correctly? O R(p) = (8000 + 5000)p – 100p? O R(p) (8000 100p) * p O R(p) (50 - p) * 8000 20p OR(p) 100p? – 20p – 200.000 O R(p) 8000p * 50 - 100 20 p likle: >809A)The variation of the total production cost with the production rate for a process is defined as follows. ALL = 2 000 000 + 4q + 2.5 q1.1 (ECU / year) q [=] kg / year a) Plot the change of total production cost according to the production speed. b) Find the annual fixed and variable costs for the case where the production rate is 2 000 000 kg / year. c) Find the average and interface costs for the same production capacity. d) If the market selling price of the product is 20 ECU/ unit, what should be the minimum production rate in order not to damage the organization?