Assume that the linear cost and revenue models apply. An item costs $4 to make. If fixed costs are $3400 and profits are $28600 when 1000 items are made and sold, find the revenue equation. (Let x be the number of items.) R(X) = %3D
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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.Rerun the new car simulation from Example 11.4, but now use the RISKSIMTABLE function appropriately to simulate discount rates of 5%, 7.5%, 10%, 12.5%, and 15%. Comment on how the outputs change as the discount rate decreases from the value used in the example, 10%.A company has determined that its profit for a product can be described by a linear function.The profit from the production and sale of 150 units is $455, and the profit from250 units is $895.(b) You are the CEO for a lightweight compasses manufacturer. The demandfunction for the lightweight compasses is given by p = 40 − 4q2where qis the number of lightweight compasses produced in millions.It costs the company $15to make a lightweight compass.(i) Write an equation giving profit as a function of the number of lightweight compassesproduced.(ii) At the moment the company produces 2 million lightweight compasses and makes a profitof $18,000,000, but you would like to reduce production. What smaller number oflightweight compasses could the company produce to yield the same profit?
- A person sells and installs A, B and C. The table shows, for example, that it takes 3 hours to sell a unit of B, it takes 4 hours to install it, and net profit per unit is $ 40. Product No. of Units Selling Hours per Unit Installation Hours per Unit Profit per Unit A x 1 1 $10 B y 3 4 40 C z 2 1 10 During a 38-hour week, the person allots no more than 18 hours to selling and no more than 20 hours to installation. Find the combination of number of units of A, B, C that would yield maximum profit.4. A publisher prints copies of a popular weekly tabloid for distribution and sale. The fixed costs are $500 per print run, with each copy printed costing an additional $0.40. If C(q) is the cost function (in $) of the price of the print run as a function of copies printed, what is the formula for C(q)? Select one: a. C(q) = 500 + 0.4q b. C(q) = 500q + 0.4 c. C(q) = (500 + 0.4)q d. C(q) = 500 - 0.4q e. C(q) = 500q - 0.4 5. A hot dog vendor sells an average of 50 hot dogs during a Little League baseball game. If the sales are Normally distributed with a standard deviation of 7 hot dogs, what is the probability the vendor will sell between 45 and 65 hot dogs? Select one: a. 74.50% b. 92.36% c. 99.78% d. 174.50% e. 2.14 f. -0.71 g. 0.71A market analyst working for a small appliance manufacturer finds that if the firm produces and sells x blenders annually, a model for the total profit (in dollars) is P(x) = 8x + 0.3x2 − 0.001x3 − 372. Graph the function P in an appropriate viewing rectangle, and use the graph to answer the following questions. (a) When just a few blenders are manufactured, the firm loses money (profit is negative). (For example, P(10) = −263, so the firm loses $263.00 if it produces and sells only 10 blenders.) How many blenders must the firm produce to break even? (Round your answer to the nearest whole number.) blenders(b) Does profit increase indefinitely as more blenders are produced and sold? YesNo If not, what is the largest possible profit the firm could have? (If profit increases indefinitely, enter your answer as ∞. Otherwise, round your answer to the nearest cent.)
- 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 ExcelI own a single share of Wivco stock. I must sell myshare at the beginning of one of the next 30 days. Each day,the price of the stock changes. With probability q(x), theprice tomorrow will increase by x% over today’s stock price(x can be negative). For example, with probability q(5),tomorrow’s stock price will be 5% higher than today’s. Showhow dynamic programming can be used to determine astrategy that maximizes the expected revenue earned fromselling the share of Wivco stock. Assume that at thebeginning of the first day, the stock sells for $10 per share.Sodaco is considering producing a new product:Chocovan soda. Sodaco estimates that the annual demandfor Chocovan, D (in thousands of cases), has the followingmass function: P(D 30) .30, P(D 50) .40,P(D 80) .30. Each case of Chocovan sells for $5 andincurs a variable cost of $3. It costs $800,000 to build aplant to produce Chocovan. Assume that if $1 is receivedevery year (forever), this is equivalent to receiving $10 atthe present time. Considering the reward for each action andstate of the world to be in terms of net present value, useeach decision criterion of this section to determine whetherSodaco should build the plant.
- If a company employs n salespersons, its gross sales in thousands of dollars may be regarded as a random vari-able having a gamma distribution with α = 80√n and β = 2. If the sales cost is $8,000 per salesperson, how many salespersons should the company employ to maxi-mize the expected profit?Assume the demand for a company’s 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 soldfor $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.you are thinking of opening a small copy shop. It costs $5000 to rent a copier for a year, and it cost $0.03 per copy to operate the copier. Other fixed costs of running the store withh amount to $400 per month. You plan to charge $0.10 per copy, and the store will be open 365 days per year. Each copier can make up to 100,000 copies per year. a. for one to five copiers rented and daily demands of 500, 1000, 1500, 2000 copies perday, find annual profit. That is, find annual profit for each of these combinations of copiers rented and daily demand. b. if you rent three copies, what daily demand for copies will allow you to break even? c. Graph profit as a function of the number of copiers for a daily demand of 500 copiers; for a daily demand of 2000 copies. Interpret your graph