A firm is considering importing some products to sell in a local market. The unit price and cost for product i are p; and Cį, respectively. While the prices may be determined by the firm, the costs are given and fixed. For product i, the demand volume is Aį – Bipi, where A; and Bi are all given. The amount of budget that may be used to purchase all products is K. The demand volume may be fractional. Formulate a mathematical program that can find a purchasing plan that maximizes the firm's profit. Determine whether your program is an LP, IP, or NLP.
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A firm is considering importing some products to sell in a local market. The unit price and cost for product i are p; and Cį, respectively. While the prices may be determined by the firm, the costs are given and fixed. For product i, the demand volume is Aį – Bipi, where A; and Bi are all given. The amount of budget that may be used to purchase all products is K. The demand volume may be fractional. Formulate a mathematical program that can find a purchasing plan that maximizes the firm's profit. Determine whether your program is an LP, IP, or NLP.
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- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.The IRR is the discount rate r that makes a project have an NPV of 0. You can find IRR in Excel with the built-in IRR function, using the syntax =IRR(range of cash flows). However, it can be tricky. In fact, if the IRR is not near 10%, this function might not find an answer, and you would get an error message. Then you must try the syntax =IRR(range of cash flows, guess), where guess" is your best guess for the IRR. It is best to try a range of guesses (say, 90% to 100%). Find the IRR of the project described in Problem 34. 34. Consider a project with the following cash flows: year 1, 400; year 2, 200; year 3, 600; year 4, 900; year 5, 1000; year 6, 250; year 7, 230. Assume a discount rate of 15% per year. a. Find the projects NPV if cash flows occur at the ends of the respective years. b. Find the projects NPV if cash flows occur at the beginnings of the respective years. c. Find the projects NPV if cash flows occur at the middles of the respective years.A company manufacturers a product in the United States and sells it in England. The unit cost of manufacturing is 50. The current exchange rate (dollars per pound) is 1.221. The demand function, which indicates how many units the company can sell in England as a function of price (in pounds) is of the power type, with constant 27556759 and exponent 2.4. a. Develop a model for the companys profit (in dollars) as a function of the price it charges (in pounds). Then use a data table to find the profit-maximizing price to the nearest pound. b. If the exchange rate varies from its current value, does the profit-maximizing price increase or decrease? Does the maximum profit increase or decrease?
- In the financial world, there are many types of complex instruments called derivatives that derive their value from the value of an underlying asset. Consider the following simple derivative. A stocks current price is 80 per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, let P be the price of the stock in a month. If P is between 75 and 85, the derivative is worth nothing to you. If P is less than 75, the derivative results in a loss of 100(75-P) dollars to you. (The factor of 100 is because many derivatives involve 100 shares.) If P is greater than 85, the derivative results in a gain of 100(P-85) dollars to you. Assume that the distribution of the change in the stock price from now to a month from now is normally distributed with mean 1 and standard deviation 8. Let EMV be the expected gain/loss from this derivative. It is a weighted average of all the possible losses and gains, weighted by their likelihoods. (Of course, any loss should be expressed as a negative number. For example, a loss of 1500 should be expressed as -1500.) Unfortunately, this is a difficult probability calculation, but EMV can be estimated by an @RISK simulation. Perform this simulation with at least 1000 iterations. What is your best estimate of EMV?If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.The accompanying table shows a bookstore's estimated demand for a new calendar. The bookstore needs to decide whether to order100, 200, or 300 calendars for the start of the year. Each calendar costs the store$5 to purchase and can be sold for $13. The store can sell any unsold calendars back to its supplier for $3 each. Determine the number of calendars the bookstore should order to maximize its expected monetary value. Demand Probability 100 0.35 200 0.25 300 0.40 The bookstore should order---------calendars in order to have the maximum expected monetary value of $----- (Type a whole number.)
- In the United States, the capital share of GDP is about 30 percent; the average growth in output is about 3 percent per year, the depreciation rate is about 4 percent per year; and the capital-out- pút ratio is about 2.5. Suppose that the produc- tion function is Cobb-Douglas, so that the capi- tal share in output is constant, and that the United States has been in a steady state.A company manufactures two products. If it chargesprice pi for product i, it can sell qi units of product i,where q1 = 60 - 3p1 + p2 and q2 = 80 - 2p2 + p1. Itcosts $5 to produce a unit of product 1 and $12 to produce a unit of product 2. How many units of eachproduct should the company produce, and what pricesshould it charge, to maximize its profit? Use spreadsheet modelling in ExcelIn the United States, the capital share of GDP is about 30 percent; the average growth in output is about 3 percent per year; the depreciation rate is about 4 percent per year, and the capital-out- pút ratio is about 2.5. Suppose that the produc- tion function is Cobb-Douglas, so that the capi- tal share in output is constant, and that the United States has been in a steady state. a. What must the saving rate be in the initial steady state? [Hint: Use the steady-state rela- tionship, sy = (8 + n + g)k.]
- Condo Construction Company is going to First NationalBank for a loan. At the present time, the bank is willing to lendCondo up to $1 million, with interest costs of 10%. Condobelieves that the amount of borrowed funds needed during thecurrent year is normally distributed, with a mean of $700,000and a standard deviation of $300,000. If Condo needs to borrowmore money during the year, the company will have to go toLouie the Loan Shark. The cost per dollar borrowed fromLouie is 25¢. To minimize expected interest costs for the year,how much money should Condo borrow from the bank?Consider a buying firm and a supplier negotiating terms for a contract. Suppose the Marginal Benefit to the buying firm of additional contract provisions in a contract (x) to the firm is: MB = 20,000 – 400x. Suppose the Marginal Cost to the buying firm of additional contract provision to the firm is: MC = 100x. What is the optimal number of contract provisions? Reconsider the previous question. If the maximum value (or price) of the contract that the buying firm is willing to pay for is $3,000, what would you expect the firm to do? a) Use the spot market b) Vertically integrate c) Continue to contract d) engage in holdupIn the Keynesian cross model, assume that the consumption function is given by:C = 100 + 0.7(Y – T)Planned investment is 300, government purchases and taxes are both 500 (initially a balanced budget)Carry all calculations to two decimal places.a. Graph “planned expenditure” as a function of income.b. What is equilibrium income?c. If government purchases increase to 550, what is the new equilibrium income? What is the income multiplier for government purchases?d. Based on your answer to the income multiplier in part c, what change in the level of government purchases is needed to achieve a new, higher level of income of 2200 (taxes unchanged at 500).e. Based on the tax multiplier from question 2, what change in the level of taxes is needed to achieve a new, higher level of income of 2200? (government purchases remain at 500)