How to Calculate Cost and Revenue Functions

What are the cost and revenue functions for a company that produces thing-a-ma-bobs?

Given that the start-up cost is $38876, the cost to make each thing-a-ma-bob is $3.39, and the selling price is $5.79 per thing-a-ma-bob.

Cost Function:

C(x) = 38876 + 3.39x

Revenue Function:

R(x) = 5.79x

The cost function, denoted as C(x), represents the total cost for producing x thing-a-ma-bobs. It includes the fixed start-up cost of $38876 and the variable cost per unit of $3.39. The formula is C(x) = 38876 + 3.39x.

On the other hand, the revenue function, denoted as R(x), illustrates the total revenue generated by selling x thing-a-ma-bobs at the price of $5.79 each. The revenue function is expressed as R(x) = 5.79x.

To determine the minimum number of thing-a-ma-bobs that the company must produce and sell to make a profit, we need to find when the revenue surpasses the cost. Therefore, we solve the inequality 5.79x > 38876 + 3.39x to find x > 16070. As a result, the company must produce and sell at least 16071 thing-a-ma-bobs to start making a profit.