The price p (in dollars) and the quantity x sold of a certain product obey the d

Question

The price p (in dollars) and the quantity x sold of a certain product obey the demand equation p=-7x +200. Answer parts (a) through e). (a) Find a model that expresses the revenue R as a function of x. (Remember, R xp.) R(x) : (Use integers or fractions for any numbers in the expression.) (b) What is the domain of R? OA. The domain is xSx O B. The domain is the set of all real numbers. (c) What is the revenue if 200 units are sold? Re $L (Round to the nearest hundredth as needed.) (d) What quantity x maximizes revenue? x= units What is the maximum revenue? (e) What price should the company charge to maximize revenue? p=$

Explanation / Answer

a)

R(x) =x*p

R(x) = (-1/7)x^2 +200x

b)

Since quantity sold will be nonnegative, interval is

{x| 0<=x<= }

c)

R(200) = (-1/7)*200^2 +200*200

=34285.71

d)

x =-b/2a

= -200/(2*-1/7)

=700 units

R(700) =$ 70000

e)

p=(-1/7)*700+200

= $100

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