Question

A deli owner has determined that his revenue, y, from selling sandwiches each day is at most - 0.05x^2 + 6, where x represents the number of sandwiches he sells. To make a profit, his revenue must be greater than his costs, represented by the expression 1.5x + 45.

What is the cost function for the deli owner?
A. C(x) = -0.05x^2 + 6
B. C(x) = 1.5x + 45
C. C(x) = -0.05x^2 + 1.5x + 45
D. C(x) = 1.5x - 0.05x^2 + 6

Answer 1

The cost function for the deli owner is represented by C(x) = 1.5x + 45, which corresponds to option B.

Thus option b is correct

Step-by-step explanation:

To find the cost function, we start with the expression for revenue, which is given as at most -0.05
`x^2` + 6. To determine the cost function, we need an expression that represents the costs. The given expression for costs is 1.5x + 45.

The revenue function is at most -0.05
`x^2` + 6, and for the deli owner to make a profit, the revenue must be greater than the costs. The costs are represented by 1.5x + 45. Therefore, the cost function is C(x) = 1.5x + 45, corresponding to option B.

To briefly explain, the revenue function given represents the maximum revenue the deli owner can make from selling sandwiches, while the cost function represents the costs associated with selling those sandwiches. The deli owner aims to ensure that the revenue surpasses the costs to yield a profit. In this case, the expression 1.5x + 45 represents the cost function, as stated in option B, satisfying the condition for the deli owner to make a profit when the revenue exceeds this cost function.

Therefore option b is correct.