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.
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.
1 answer:
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.
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