Question

To earn a profit, the revenue must be greater than the cost. The revenue for selling x units of an item is R = 26.05x. The cost to make x units is C = 1,500 + 16.75x. The owner claims she had a profit today because they made and sold 183 units of the item. Is her claim true?
a. Yes, because R > C when x = 183.

b. Yes, because R < C when x = 183

c. No, because R > C when x = 183.

d.No, because R < C when x = 183.

Answer 1

Answer:

a. Yes. The owner made a profit, because R > C when x = 183.

Step-by-step explanation:

(1) Calculate the revenue

R = 26.05x = 26.05 × 183 = 4767.15

(2) Calculate the cost

C = 1500 + 16.75x = 1500 + 16.75 ×183 = 1500 + 3065.25 = 4565.25

(3) Calculate the profit

P = R – C = 4767.1 – 4565.25 = 201.90

P > 0. The owner made a profit, because R > C when x = 183.

In the graphs below, the red line represents costs and the blue line represents revenues.

We see that C > R until we reach the break-even point at 162 units. After 162 units, R > C, and the business makes a profit. This, making 183 units is profitable for the company.