It costs 1212 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 2 over x minus 12 endfraction plus 7 (100 minus x )n= 2 x−12+7(100−x). find the selling price that will maximize profit.

The selling price that will maximize profit is $56.

Step-by-step explanation:

Given : It costs 12 dollars to manufacture and distribute a backpack. If the backpacks sell at x dollars each, the number sold, n, is given by

To find : The selling price that will maximize profit ?

Solution :

The cost price is $12.

The selling price is $x

Profit = SP-CP

Profit = x-12

The profit of n number is given by,

Substitute the value of n,

Derivate w.r.t x,

Put it to zero for critical point,

Derivate again w.r.t x, to determine maxima and minima,

It is a maximum point.

Therefore, the selling price that will maximize profit is $56.

d is correct

step-by-step explanation: