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

To find the level of production that maximizes profit, we need to find the maximum of the given profit function. We can do this by taking the derivative of the profit function with respect to the number of units produced (e), setting it equal to zero, and solving for e.

Profit function: 11e - 0.3e^2 - 500

First derivative: 11 - 0.6e

Setting the first derivative equal to zero: 
11 - 0.6e = 0 
e = 18.33

Since we can't physically produce 18.33 units, we round down to the nearest whole number, which is 18. Therefore, a production level of 18 units will maximize profit. However, this is not one of the answer choices.

The closest answer choice is D, a production level of 50 units. We can check that this is a maximum by using the second derivative test.

Second derivative: -0.6

Since the second derivative is negative, this confirms that we have a maximum at e = 50. Therefore, the best choice is D, a production level of 50 units.

The Daily Profit from the Sale of a Product Is