For the demand equation, express the total revenue R as a function of the price p per item. q = -6p + 600 R(p) = Sketch the graph of the resulting function. 20000 Graph Layers 19000 Clear All 18000 After you add an object to the graph 17000 16000 can use Graph Layers to view and ed 15000 properties. 14000 Fill 13000 12000 11000 1000 9000 8000 7000 No 6000 Solution 5000 4000 3000 2000 1000 -10 10 20 30 40 50 60 70 80 90 100 110 -1000 -200 Help WebAssign. Graphing Tool Determine the price p (in dollars) that maximizes total revenue.Revenue Pack-Em-In has another development in the works. If it builds 50 houses in this development, it will be able to sell them at $380,000 each, but if it builds 120 houses, it will get only $240,000 each. Obtain a linear demand equation. (Let p be the price of a house and q the number of houses.) p(q) = Determine how many 1ouses it should build to get the largest revenue. What is the largest possible revenue (in dollars)? $: T-Shirt Prot Two fraternities, Sig Ep and Ep Sig, plan to raise money jointly to benet homeless people on Long Island. They will sell Yoda vs. Alien T-shirts in the student center, but are not sure how much to charge. Sig Ep treasurer Augustus recalls that they once sold 240 shirts in a week at $7 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 550 per week at $3 per shirt. (a) On the oasis of this information, construct a linear demand equation for Yoda vs. Alien T-shirts. Hence obtain the weekly revenue R as a function of the unit price x. R(x) = (b) The university administration charges the fraternities a weekly fee of $300 for use of the student center. Write down the weekly prot P as a function of the unit price x. P(X) = Determine how much the fraternities should charge (in dollars per T-shirt) to obtain the largest possible weekly prot. What is the largest possible weekly prot (in dollars)? $: Find the time required, to the nearest 0.1 year, for the investment to reach the desired goal. $3,000 invested at 7%, compounded monthly; goal: $5,000 Some time ago, a consultant formulated the following linear model of demand for online novels, where q is the monthly demand for an online bookstore's online novels at a price of p dollars per novel. q = 60p + 960 (a) Use this model to express the monthly revenue R as a function of the unit price p. R03) = Hence, determine the price you should charge for a maximum monthly revenue. (Round your answer to the nearest cent.) $|:| (b) Author royalties and copyright fees cost the company an average of $3 per novel, and the monthly cost of operating and maintaining the online publishing service amount. to $900 per month. Express the monthly prot P as a function of the unit price p. Plp) = Hence, determine the unit price you should charge for a maximum monthly prot. (Round your answer to the nearest cent.) $|:| What is the resulting prot (or loss)? (Round your answer to the nearest cent.) $ll Find the future value of the investment. (Round your answer to the nearest cent.) $3,000 for 6 years at 4.25% simple annual interest 5;: Find the present value of the investment. (Round your answer to the nearest cent.) funding $4,000 withdrawals at the end of each half-year for 2.5 years at 5.25% interest compounded semiannually 3;: Find the time, to the nearest 0.1 year. the time it would take $5,000 to grow to $12,000 at 4.75% simple annual interest yrOHaganBooks.com is seeking a $250,000 loan to finance its continuing losses. One of the best deals available is offered by Industrial Bank, which offers a 10-year 8.5% loan. What would the monthly payments be for this loan? (Assume interest is compounded monthly. Round your answer to the nearest cent.) $|:| Graph the given equation. y = 3x - 4 Graph Clear Al After Delete can u prop O Fill 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 2 3 4 5 6 7 8 9 10 No Solution Help WebAssign. Graphing ToolFind the periodic withdrawals PMTfor the given annuity account. HINT [See Quick Example 4.] (Assume endofperiod withdrawals and compounding at the same intervals as withdrawals. Round your answer to the nearest cent.) $35,000 at 3%, paid out quarterly for 15 years mm: Determine the periodic payments PMT on the given loan or mortgage. (Round your answer to the nearest cent.) $90,000 borrowed at 7% for 10 years, with monthly payments we: Jennifer's pension plan is an annuity with a guaranteed return of 5% per year (compounded monthly). She can afford to put $300 per month into the fund, and she will work for 40 years before retiring. If her pension is then paid out monthly based on a 20-year payout, how much will she receive per month? (Round your answer to the nearest cent.) $E Determine the periodic payments on the given mortgage. HINT [See Example 5.] (Round your answer to the nearest cent.) a $1,000,000, 32-year, 5.1% mortgage with monthly payments 3;: Find a linear equation whose graph is the straight line with the given properties. through (2, 3) and (1, 1) x} A large department store is prepared to buy 3,800 of your tie-dye shower curtains per month for $4 each, but only 3,650 per month for $9 each. What is the linear demand function for your tie- dye shower curtains? W?) = The following table shows worldwide sales of a certain type of cell phone and their average selling prices in 2012 and 2013. (a) Use the data to obtain a linear demand function for this type of cell phone. (Letp be the price, and let q be the demand). alp) = Use your demand equation to predict sales if the price is lowered to $275. : million phones (b) Fill in the blank. For every $1 increase in price, sales of this type of cell phone decrease by S million units. The demand for your college newspaper is 5,000 copies each week if the paper is given away free of charge, and drops to 4,000 each week if the charge is 10 per copy. However, the university is prepared to supply only 800 copies per week free of charge, but will supply 1,600 each week at 20 per copy. (a) Write down the associated linear demand and supply functions. (,0 is in dollars.) demand function q(p) supply function q(p) (b) At what price (in dollars) should the college newspapers be sold so that there is neither a surplus nor a shortage of college newspapers? $: Equilibrium Price: Cell Phones Worldwide quarterly sales of a brand of cell phones were approximately :7 = p + 146 million phones when the wholesale price was $p. (a) [f the cellphone company was prepared to supply q = 9p 394 million phones per quarter at a wholesale price of $p, what would have been the equilibrium price? $ E (b) The actual wholesale price was $49 in the fourth quarter of 2004. Estimate the projected shortage or surplus at that price. There is an estimated of: million phones. Demand for Smartphones The following table shows worldwide sales of a type of phone and their average selling prices in 2012, 2013, and 2017 Year 2012 2013 2017 Selling Price p ($100) 4 3 2 Sales q (billions) 0.5 1 2 Find the regression line (round coefficients to one decimal place). q(p) = Use the regression line to estimate the demand (in millions of units sold) when the selling price was $320. million