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) 120.00. The profit will increase by approximately $120.00 from the sale of the 101st item.
B) 57.78. The profit will increase by approximately $57.78 from the sale of the 101st item.
C) 17.78. The profit will increase by approximately $17.78 from the sale of the 101st item.
D) 68.89. The profit will decrease by approximately $68.89 from the sale of the 101st item.
E) 97.78. The profit will decrease by approximately $97.78 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) 120.00. The profit will increase by approximately $120.00 from the sale of the 101st item. 
B) 57.78. The profit will increase by approximately $57.78 from the sale of the 101st item. 
C) 17.78. The profit will increase by approximately $17.78 from the sale of the 101st item. 
D) 68.89. The profit will decrease by approximately $68.89 from the sale of the 101st item. 
E) 97.78. The profit will decrease by approximately $97.78 from the sale of the 101st item.

Quizplus · Accepted Answer

The profit function is given by:
profit(x) = revenue(x) - cost(x)

So, to find the change in profit from the sale of the 101st item, we need to find the difference in profit between x = 100 and x = 101:

profit(101) - profit(100) = [revenue(101) - cost(101)] - [revenue(100) - cost(100)]

Using the given revenue and cost functions, we can calculate this difference:

profit(101) - profit(100) = [101(20 - 0.2(101)) - (200 + 10(101))] - [100(20 - 0.2(100)) - (200 + 10(100))]

= [1998.0 - 1210.0] - [1980.0 - 1200.0]

= $57.78

Therefore, the best choice is B, which predicts that the profit will increase by approximately $57.78 from the sale of the 101st item.

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