Question

A manufacture has been selling 1800 television sets a week at $390 each. A market survey indicates that for each $10 rebate offered to a buyer, the number of sets sold will increase by 100 per week.

a) Find the function representing the demand p(x), where x is the number of the television sets sold per week and p(x) is the corresponding price. p(x) =

b) How large rebate should the company offer to a buyer, in order to maximize its revenue? dollars

c) If the weekly cost function is 117000 + 130x, how should it set the size of the rebate to maximize its profit? dollars

Answer 1

PART(a):

The slope of the line is given by,

The equation of the line is given by,

Hence the demand eqn is given by,

PART(b):

The revenue is given by,

diff wrt x,

For maximum revenue,

Now the price becomes,

Hence the size of the rebate would be,

PART(c):

we have,

and the cost function is given by,

The profit function is given by,

diff wrt x,

For maximum profit,

Now the price is given by,

Hence the size of the rebate would be,

I hope this answer helps,
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