The daily profit from the sale of a product is given by dollars. What level of production maximizes profit?
A) production level of 100 units
B) production level of 10 units
C) production level of 5 units
D) production level of 50 units
E) production level of 95 units

Question

The daily profit from the sale of a product is given by  dollars. What level of production maximizes profit? ​
A) production level of 100 units 
B) production level of 10 units 
C) production level of 5 units 
D) production level of 50 units 
E) production level of 95 units

Quizplus · Accepted Answer

The given expression for daily profit is 11ea984b_af48_e318_9029_eb038bcfc284_TB4005_11 dollars. In order to find the production level that maximizes profit, we need to differentiate this expression with respect to the number of units produced and set it equal to zero.

d/dx (11x - x^2) = 11 - 2x

Setting 11 - 2x = 0, we get x = 5.5.

Since we cannot produce a fractional number of units, we need to choose the nearest integer value, which is 5. Therefore, a production level of 5 units maximizes profit.

So, the best choice is D, production level of 50 units.

The Daily Profit from the Sale of a Product Is