1) Suppose that the profit (in dollars) from the production and sale of x units of a product is given by

P(x) = 180x ? x² / 100 - 200

In addition, suppose that for a certain month the number of units produced on day t of the month is

x = q(t) = 850 + 10t.

(a) Find

(P ? q)(t)

to express the profit (in dollars) as a function of the day of the month.

(P ? q)(t) =

(b) Find the number of units produced, and the profit, on the thirteenth day of the month.

Units Produced:

Profit:

2)If a test that has reliability r is lengthened by a factor n (n ? 1), the reliability R of the new test is given by

R(n) = nr/1+(n-1)r 0 <>r ? 1

If the reliability is r = 0.6, the equation becomes

R(n) = 0.6(n) / 0.4 + 0.6(n)

(a) Find R(1). .

R(1) =

(b) Find R(2); that is, find R when the test length is doubled.

R(2) =

(c) What percent improvement is there in the reliability when the test length is doubled?