Question

Use a daily production cost C for x units.

A manufacturer of gas grills has daily production costs of

C = 400 – 5x + 0.125x2, where x is the number of gas grills produced. How many units should be produced each day to yield a minimum cost?

units should be produced each day to yield a minimum cost.

Answer 1

To find the number of units that should be produced each day to yield a minimum cost, we need to determine the value of x that minimizes the daily production cost function C.

The daily production cost function is given by:
C = 400 - 5x + 0.125x^2

To find the minimum cost, we can take the derivative of the cost function with respect to x and set it equal to zero. Then we solve for x.

Taking the derivative of C with respect to x:
dC/dx = -5 + 0.25x

Setting the derivative equal to zero and solving for x:
-5 + 0.25x = 0
0.25x = 5
x = 20

So, the minimum cost will be achieved when 20 units are produced each day.