Question

A manufacturer of lighting fixtures has daily production costs of C 800 - 50x+ 0.25x2, where C is the total cost (in dollars) and x is the number of units produced. What daily production number

yields a minimum cost?
x fixtures
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Answer 1

To find the daily production number that yields a minimum cost, we need to find the value of x that minimizes the cost function C(x) = 800 - 50x + 0.25x^2.

We can find the minimum point of the quadratic function by using the formula:

x = -b/(2a)

where a = 0.25, b = -50.

Substituting these values into the formula, we get:

x = -(-50)/(2*0.25)
x = 100

Therefore, the daily production number that yields a minimum cost is 100 fixtures.