Question

You invested $30,000 and started a business writing greeting cards. Supplies cost $0.02 per card, x, and you are selling each card for $0.50. What is the cost function, C(x)?

A) C(x) = 0.50x + $30,000
B) C(x) = 0.48x + $30,000
C) C(x) = 0.02x - $30,000
D) C(x) = $30,000 - 0.48x

Answer 1

The cost function for the greeting card business is C(x) = 0.02x + $30,000, combining both the fixed initial investment and the variable supplies cost per card produced.

Step-by-step explanation:

The student's question concerns finding the cost function for their greeting card business. Given that the initial investment was $30,000, which is a fixed cost, and the cost of supplies is $0.02 per card (represented by x), we can determine the cost function, C(x). The correct cost function would include both the fixed cost and the variable cost per card produced:

C(x) = Fixed Cost + (Cost per card) * x
C(x) = $30,000 + $0.02x

This is a linear function showing how the total cost depends on the number of cards, x, produced. Therefore, the correct answer is C(x) = 0.02x + $30,000.