Question

A factor produces luggage. As production increases, the cost decreases. The cost for producing "x" units of luggage can be approximated according to c(x) = 0.04x^2 - 8.504x + 25302.

a. How many units should be produced to minimize cost?
A. 106
B. 211
C. 318
D. 424
b. What is the minimum cost?
A. $6,010.25
B. $6,748.72
C. $7,183.50
D. $7,956.81

Answer 1

a. The number of units to minimize cost is 211.

b. The minimum cost is $6,748.72.

Step-by-step explanation:

To determine the number of units that minimize cost, we use calculus. The given cost function, c(x) = 0.04x^2 - 8.504x + 25302, represents the cost for producing x units of luggage. To find the minimum cost, we derive the function to find its critical point. By taking the derivative of c(x) and setting it to zero (c'(x) = 0), we find the value of x that minimizes cost. In this case, x = 211 units minimizes the cost.

Substituting x = 211 into the cost function c(x) gives us the minimum cost. Plugging this value into the cost function provides the minimum cost of $6,748.72. Therefore, to minimize production costs, 211 units of luggage should be produced, resulting in a cost of $6,748.72.