Question

The cost C (in dollars) for ordering and storing x units is C=8x+500,000/x . What order size will produce a minimum x= units

Answer 1

To find the order size that will produce a minimum cost, we need to find the value of x that minimizes the cost function. Taking the derivative of the cost function with respect to x, setting it equal to zero, and solving for x gives us x ≈ 353.

Step-by-step explanation:

The cost function is given as C = 8x + 500,000/x. To find the order size that will produce a minimum cost, we need to find the value of x that minimizes the cost function. To do this, we can take the derivative of the cost function with respect to x and set it equal to zero.

Taking the derivative of C with respect to x, we get dC/dx = 8 - 500,000/x2. Setting this derivative equal to zero and solving for x, we get 8 - 500,000/x2 = 0.

Simplifying this equation, we have 8x2 - 500,000 = 0. Solving for x, we find that the order size that will produce a minimum cost is x = sqrt(500,000/8) or x ≈ 353.