6. [-/2 Points] DETAILS Crude oil imports to one country from another for 2009-2013 could be approximated by the following model where & is time in years since the start of 2000. I(t) = -33to + 800t - 1,000 thousand barrels per day (9 s t s 13) According to the model, approximately when were oil imports to the country greatest? HINT [See Example 1.] (Round your answer to two decimal places.) t = How many barrels per day were imported at that time? (Round your answer to two significant digits.) thousand barrels Need Help? Read It8. [-/2 Points] DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Revenue The Better Baby Buggy Co. has just come out with a new model, the Turbo. The market research department predicts that the demand equation for Turbos is given by q = -3p + 228, where q is the number of buggies the company can sell in a month if the price is $p per buggy. At what price (in dollars) should it sell the buggies to get the largest revenue? P = $ What is the largest monthly revenue (in dollars)? $ Need Help? Read It Watch It 9. [-/4 Points] DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Website Profit You operate a gaming website, www.mudbeast.net, where users must pay a small fee to log on. When you charged $3 the demand was 580 log-ons per month. When you lowered the price to $2.50, the demand increased to 870 log-ons per month. (a) Construct a linear demand function for your website and hence obtain the monthly revenue R as a function of the log-on fee x. R (x ) = (b) Your Internet provider charges you a monthly fee of $50 to maintain your site. Express your monthly profit Pas a function of the log-on fee x. P (x ) = Determine the log-on fee you should charge to obtain the largest possible monthly profit (in dollars). x = $ What is the largest possible monthly profit (in dollars)? $10. [-/4 Points] DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER T-Shirt Profit The latest demand equation for your Yoda vs. Alien T-shirts is given by 4 = -50x + 800 where q is the number of shirts you can sell in one week if you charge $x per shirt. The Student Council charges you $100 per week for use of their facilities, and the T-shirts cost you $6 each. Find the weekly cost as a function of the unit price x. C(x) = Hence, find the weekly profit as a function of x. P (x) = Determine the unit price (in dollars per T-shirt) you should charge to obtain the largest possible weekly profit. x = $ per T-shirt What is the largest possible weekly profit (in dollars)? $ Need Help? Read It Watch It11. [-/6 Points] DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Television Advertising As Sales Manager for Montevideo Productions, Inc., you are planning to review the prices you charge clients for television advertisement development. You currently charge each client an hourly development fee of $2,900. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 21 contracts. This is down 6 contracts from the figure last year, when your company charged only $2,300. (a) Construct a linear demand equation giving the number of contracts 4 as a function of the hourly fee p Montevideo charges for development. q(p) = (b) On average, Montevideo bills for 40 hours of production time on each contract. Give a formula for the total revenue obtained by charging $p per hour. R(P) = (c) The costs to Montevideo Productions are estimated as follows. Fixed costs: $150,000 per month Variable costs: $60,000 per contract Express Montevideo Productions' monthly cost as a function of the number q of contracts. c(9) = Express Montevideo Productions' monthly cost as a function of the hourly production charge p. C(p) = (d) Express Montevideo Productions' monthly profit as a function of the hourly development fee p. P (p) = Find the price it should charge to maximize the profit (in dollars per hour). P = $ per hour Need Help? Read It Watch It12. [HI Points] DETAILS PREVIOUS ANSWERS IF the revenue Function For a particular n:ornn'|o|:iii:g,.r is Rip] = 53,I:.I2 + 63"p. what is the {linear} demand Function ob}? Give a reason For your answer. GR=p
