1.) The cost, in millions of dollars, of building a three-story high school in N
ID: 2889935 • Letter: 1
Question
1.) The cost, in millions of dollars, of building a three-story high school in New York State was estimated to be
C(x) = 1.7 + 0.17x 0.0001x2 (20 x 400)
where x is the number of thousands of square feet. Suppose that you are contemplating building a for-profit three-story high school and estimate that your total revenue will be $0.25 million dollars per thousand square feet. What is the profit function (in millions of dollars)?
P(x) = _________________
What size school should you build in order to break even? (Round your answer to three decimal places.)
_______________thousand ft2
2.) The demand for your hand-made skateboards, in weekly sales, is q = 6p + 700 if the selling price is $p. You are prepared to supply q = 4p 400 per week at the price $p. What price should you sell your skateboards for so that there is neither a shortage nor a surplus? $ __________ per skateboard.
3.) The demand for your factory-made skateboards, in weekly sales, is q = 7p + 50 if the selling price is $p. If you are selling them at that price, you can obtain q = 3p 30 per week from the factory. At what price should you sell your skateboards so that there is neither a shortage nor a surplus? (Round your answer to the nearest cent.) $__________
4.) Worldwide quarterly sales of a brand of cell phones were approximately q = p + 136 million phones when the wholesale price was $p.
(a) If the cellphone company was prepared to supply q = 9p 374 million phones per quarter at a wholesale price of $p, what would have been the equilibrium price?
$ ______________
(b) The actual wholesale price was $46 in the fourth quarter of 2004. Estimate the projected shortage or surplus at that price.
There is an estimated ---Select--- shortage or surplus of _________million phones.
Explanation / Answer
multiple questions posted.please post each question seperately
1)
given cost C(x) = 1.7 + 0.17x 0.0001x2 million dollars . (20 x 400) where x is the number of thousands of square feet,total revenue is $0.25 million dollars per thousand square feet
=>total revenue for x thousand square feet ,R(x)= 0.25x million dollars
profit function ,P(x) =R(x)-C(x)
profit function ,P(x) =0.25x -(1.7 + 0.17x 0.0001x2 )
profit function ,P(x) = -1.7 + 0.08x + 0.0001x2 (in millions of dollars)
at break even profit is zero
=>-1.7 + 0.08x + 0.0001x2=0
=>0.0001*(-17000 + 800x + x2)=0
=>800x + x2=17000
=>x2+800x+(800/2)2=17000+(800/2)2
=>x2+800x+4002=177000
=>(x+400)2=177000
=>x+400=420.71367935925259144109927495708
=>x=20.71367935925259144109927495708
in order to break even , size of school should be 20.714 thousand ft2
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