Final answer:
To determine the point of profit for producing and selling units, compare the revenue function R(x) to the cost function C(x) for each given option. A profit is made when R(x) is greater than C(x). Calculate these values for the provided unit options to find when the firm will be profitable.
Step-by-step explanation:
Calculating Profit for Producing and Selling Units
To determine the number of units that must be produced and sold to result in a profit, we must assess where total revenue exceeds total costs. The revenue function given by R(x) = 150x - 0.01x^2 and the cost function C(x) = 22x + 0.01x^2 + 48,000 must be analyzed. A profit occurs when revenue exceeds cost, which can be expressed as R(x) > C(x).
We will examine the options given to see which yields a profit:
- A) 5,000 units: R(5000) = 150(5000) - 0.01(5000)^2, C(5000) = 22(5000) + 0.01(5000)^2 + 48,000. After calculating, check if R(5000) > C(5000).
- B) 10,000 units: Do the same calculations for 10,000 units and compare R(10000) to C(10000).
- C) 15,000 units: Do the calculations for 15,000 units, and again, R(15000) must be greater than C(15000) for there to be a profit.
- D) 20,000 units: Finally, calculate the values for 20,000 units and determine if R(20000) exceeds C(20000).
The correct answer will be the option where R(x) is greater than C(x), indicating that the firm is making a profit.