In the “Real World”, what is the Highest value that the Selling Price could be?

Question

Let Revenue = Selling Price * Qty and Cost = Variable Cost * Qty. Suppose that the Variable Cost per unit is $12, and the Quantity Sold Depends on the Selling Price and is given by the equation Qty = 200,000 – 5000*Selling Price. 

In the “Real World”, what is the Highest value that the Selling Price could be?

In the “Real World”, what is the Lowest value for the Price P?

How much Profit would you make if your Selling Price was $20 ?

Answer 1

Let R=revenue, C=cost, Q=quantity sold, and S=selling price

R=S*Q

C=12*Q

R-C must be greater than or equal to 0

SQ-12Q≥0

(S-12)(200000-5000S)≥0

From this equation we see that S must be at least 12.

Expanding this equation and dividing it by 1000 give'

5S² - 140S + 2400 and the derivative is 10S-140 which means the maximum profit will occur when S=14.