The consumer demand equation for tissues is given by q = (108 − p)2, where p is the price per case of tissues and q is the demand in weekly sales.
(a) determine the price elasticity of demand e when the price is set at $32. (round your answer to three decimal places.) e = interpret your answer. the demand is going by % per 1% increase in price at that price level.
(b) at what price should tissues be sold to maximize the revenue? (round your answer to the nearest cent.) $
(c) approximately how many cases of tissues would be demanded at that price? (round your answer to the nearest whole number.) cases per week

a) -0.842

b) $0

c) 11,664 cases

Step-by-step explanation:

a)

The price elasticity of demand E at a given point is defined as

and in this case, it would measure the possible response of tissues demand due to small changes in its price when the price is at

When the price is set at $32 the demand is

cases of tissues, so

Also, we have

hence

That would mean the demand is going down about 0.842% per 1% increase in price at that price level.

b)

When the price is $108 the demand is 0, so the price should always be less than $108.

On the other hand, the parabola

is strictly decreasing between 0 and 108, that means the maximum demand would be when the price is 0.

c)

When the price is 0 the demand is  

cases

step-by-step explanation:

through just a quick inspection, one can see that the graph of this cubing function starts in quadrant iii and ends in quadrant i.   when x = 0, y = 3, so the y-intercept is (0, 3).

if graphs are part of the problem statement, share them.   .

$450 is the answer.

step-by-step explanation:

30% of 450 = 135

450-135=315