In this problem, cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total revenue function is given by , and that the total cost function is given by . Find at , and explain what it predicts. Round your answer to two decimal places.
A)130.00. The profit will increase by approximately $130.00 from the sale of the 101st item.
B)40.00. The profit will increase by approximately $40.00 from the sale of the 101st item.
C)10.00. The profit will increase by approximately $10.00 from the sale of the 101st item.
D)60.00. The profit will decrease by approximately $60.00 from the sale of the 101st item.
E)90.00. The profit will decrease by approximately $90.00 from the sale of the 101st item.

Question

In this problem, cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total revenue function is given by  , and that the total cost function is given by  . Find  at  , and explain what it predicts. Round your answer to two decimal places. ​
A)130.00. The profit will increase by approximately $130.00 from the sale of the 101st item. 
B)40.00. The profit will increase by approximately $40.00 from the sale of the 101st item. 
C)10.00. The profit will increase by approximately $10.00 from the sale of the 101st item. 
D)60.00. The profit will decrease by approximately $60.00 from the sale of the 101st item. 
E)90.00. The profit will decrease by approximately $90.00 from the sale of the 101st item.

Quizplus · Accepted Answer

We can use the formula for profit:

Profit = Revenue - Cost
P(x) = R(x) - C(x)

We are given that:
R(x) = 12x
C(x) = 4x + 800

So we can write:
P(x) = 12x - (4x + 800)
P(x) = 8x - 800

To find the profit from the sale of the 101st item, we can evaluate P(101) - P(100):

P(101) = 8(101) - 800
P(101) = 8*101 - 800
P(101) = 808 - 800
P(101) = 8

P(100) = 8(100) - 800
P(100) = 800 - 800
P(100) = 0

So P(101) - P(100) = 8 - 0 = 8

Therefore, the profit will increase by approximately $8.00 from the sale of the 101st item. Rounded to two decimal places, the answer is 8.00, which corresponds to choice B.

In This Problem, Cost, Revenue, and Profit Are in Dollars