Question

A company finds that if they price their product at $ 35, they can sell 225 items of it. For every dollar increase in the price, the number of items sold will decrease by 5.


What is the maximum revenue possible in this situation? (Do not use commas when entering the answer) $


What price will guarantee the maximum revenue? $

Answer 1

Answer:

Maximum revenue = $8000

The price that will guarantee the maximum revenue is $40

Step-by-step explanation:

Given that:

Price of product = $35

Total sale of items = 225

For every dollar increase in the price, the number of items sold will decrease by 5.

The total cost of item sold = 225 ×35

The total cost of item sold = 7875

If c should be the dollar unit in price increment;

Therefore; the cost function is : $[35+c(1)][225-5(c)]$

For maximum revenue;

$\dfrac{d}{dc}(cost \ function) =0$

$\dfrac{d}{dc}[[35+c(1)][225-5(c)]]=0$

0+225-35× 5 -10c = 0

225 - 175  =10c

50 = 10c

c = 50/10

c = 5

Maximum revenue = $[35+c(1)][225-5(c)]$

Maximum revenue = $[35+5(1)][225-5(5)]$

Maximum revenue = (35 + 5)(225-25)

Maximum revenue = (40 )(200)

Maximum revenue = $8000

The price that will guarantee the maximum revenue is :

=(35 +c)

= 35 + 5

= $40