Question

The cost, C(x), of producing x Totally Cool Coolers is modeled by the function C(x)=0.005x^2−0.5x+23. How many coolers need to be produced and sold in order to minimize the cost? (Round to the nearest whole number.)

A. The cost is at a minimum after 47 coolers are produced and sold.
B. The cost is at a minimum after 50 coolers are produced and sold.
C. The cost is at a minimum after 53
coolers are produced and sold.
D. The cost is at a minimum after 55 coolers are produced and sold.

Answer 1

The cost is at a minimum after 50 coolers are produced and sold.

Step-by-step explanation:

To find the number of coolers that need to be produced and sold in order to minimize the cost, we need to determine the x-value that corresponds to the minimum value of the function C(x) = 0.005x^2 - 0.5x + 23. This can be done by finding the vertex of the quadratic function. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function. In this case, a = 0.005 and b = -0.5. Plugging these values into the formula, we get x = -(-0.5) / (2*0.005) = 50. Therefore, the cost is at a minimum after 50 coolers are produced and sold.