The profit P in dollars per day resulting from making x unit

The profit, P, in dollars per day, resulting from making x units per day of air conditioners prior to the summer is:

P = 12.5x² + 18x 155, find the marginal profit when the production level is 10 air conditioners per hour in a 12 hour production day.

Solution

given profit P = 12.5x² + 18x 155

for marginal profit differentiate with respect to x

dP/dx =12.5*2x +18*1 -0

dP/dx =25x +18

production level is 10 air conditioners per hour in a 12 hour production day. , x=10*12=120 units

marginal profit dP/dx =(25*120) +18

marginal profit =3000+18

marginal profit =3018 dollars per unit