It costs a company c(x) dollars to produce x units. Thecurve y c (x) is called the firm’s marginal cost curve.(Why?) The firm’s average cost curve is given by z c(xx).Let x* be the production level that minimizes the company’saverage cost. Give conditions under which the marginal costcurve intersects the average cost curve at x*.
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It costs a company c(x) dollars to produce x units. The
curve y c (x) is called the firm’s marginal cost curve.
(Why?) The firm’s average cost curve is given by z
c(
x
x)
.
Let x* be the production level that minimizes the company’s
average cost. Give conditions under which the marginal cost
curve intersects the average cost curve at x*.
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- 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.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.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?
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- A company produces a component internally with a finite production rate P and the demand rate for the component is λ. The quantity needed for a production batch in period T is Q and the maximum inventory level in T is H. Use a graph to show that H will not exceed Q. Use T1 to denote uptime and T2 to denote down time.You operate a small wooden toy company making two products: alphabet blocks and wooden trucks. Your profit is $30 per box of blocks and $40 per box of trucks. Producing a box of blocks requires one hour of woodworking and two hours of painting; producing a box of trucks takes three hours of woodworking, but only one hour of painting. You employ three woodworkers and two pointers, each working 40 hours a week. How many boxes of block (B) and trucks (T) should you make each week to maximize profit? Solve graphically as a linear program and confirm analytically.An analyst is constructing a simple model to determine the gross and net profit of a product, given its profit per unit, quantity sold, and the total costs assigned to the product. The calculation for gross profit is Profit per Unit times Quantity. The calculation for Net Profit is Gross Profit minus Total Costs. A B 1 2 Profit per Unit 2 3 Quantity 19,400 4 Gross Profit 5 6 Total Costs 9,600 7 8 Net Profit With the values for Profit per Unit, Quantity, and Total Costs shown above, what should the model return for the following calculated cells