Question

It costs 6 dollars to manufacture and distribute a backpack. If the backpacks sell at x dollars​ each, the number​ sold, n, is given by n equals StartFraction 5 Over x minus 6 EndFraction plus 5 (100 minus x ). Find the selling price that will maximize profit.

Answer 1

Answer:

$53

Step-by-step explanation:

$n=\frac{5}{x-6}+5*(100-x)$

Let 'x' be the selling price. The revenue is given by 'xn' while the production cost is given by '6n' therefore, the profit function is:

$P=xn-6n=(x-6)*(\frac{5}{x-6}+500-5x))\\P=5+500x-3000-5x^2+30x\\P=-5x^2+530x-2950$

The price 'x' for which the derivate of the profit function is zero is the price that maximizes profit:

$P=-5x^2+530x-2950\\P'=0=-10x+530\\x=\ 53$

The selling price that will maximize profit is $53.