Suppose the Sunglasses Hut Company has a profit function given b..

Question

Suppose the Sunglasses Hut Company has a profit function given by
P
(
q
)
=
−
0.02
q
2
+
3
q
−
29
P(q)=-0.02q2+3q-29, where
q
q is the number of thousands of pairs of sunglasses sold and produced, and
P
(
q
)
P(q) is the total profit, in thousands of dollars, from selling and producing
q
q pairs of sunglasses.

A) How many pairs of sunglasses should be sold to maximize profits? (If necessary, round your answer to the nearest whole number of sunglasses.)      B) What are the actual maximum profits? (If necessary, round your answer to nearest whole number of dollars.)

Answer 1

Use the equation

 

h = -b / (2a)  to find the number of sunglasses.

 

where:

a = -0.02

b = 3

 

Plug in these values into the formula to find the number of sunglasses.  Then multiply the value by 1000 to get the actual amount of glasses.

 

 

Finally evaluate P(h) to find the maximum cost.  Multiply the result by 1000 to get the actual maximum cost.