Problem page
a supply company manufactures copy machines. the unit cost c (the cost in dollars to make each copy machine) depends on the number of machines made. if x machines are made, then the unit cost is given by the function c (x) = 0.5x^2-150 + 21,035. how many machines must be made to minimize the unit cost?
do not round your answer.

1 machine must be made to minimise the unit cost.

Step-by-step explanation:

Step 1: Identify the function

x is the number of machines

C(x) is the function for unit cost

C (x) = 0.5x^2-150 + 21,035

Step 2: Substitute values in x to find the unit cost

C (x) = 0.5x^2-150 + 21,035

The lowest value of x could be 1

To check the lowest cost, substitute x=1 and x=2 in the equation.

When x=1

C (x) = 0.5x^2-150 + 21,035

C (x) = 0.5(1)^2-150 + 21,035

C (x) = 20885.5

When x=2

C (x) = 0.5x^2-150 + 21,035

C (x) = 0.5(2)^2-150 + 21,035

C (x) = 20887

We can see that when the value of x i.e. the number of machines increases, per unit cost increases.

Therefore, 1 machine must be made to minimise the unit cost.

!!