Question

22. The function C= 75x + 2600 gives the cost, in dollars, for a small company to

manufacture x items. The function R = 225x-X gives the revenue, also in
dollars, for selling x items. How many items should the company produce so
that the cost and revenue are equal?

Answer 1

Given:

`c=75x+2600\\`; where c is cost in dollars and x is items sold

`r=225x-x^(2)`; where r is revenue in dollars and x is items sold

Equations:

`x=(-b\±√(b^2-4ac))/(2a)`

Answer:

For cost and revenue to be equal, the company should produce and sell 20 or 130 items.

`x=20\\` or
`x=130`

Explanation:

1. Set the equations equal to each other;
`75x+2600=225x-x^2`

2. Subtract
`225x-x^2` from each side;
`x^2-150x+2600=0\\`

3. Determine quadratic formula variables;
`a=1; b=-150; c=2600`

4. Substitute
`a`,
`b`, and
`c` into quadratic formula;
`x=(-(150)\±√((-150)^2-4*1*260))/(2*1)`

5. Solve quadratic formula;
`x_(1) = 130`,
`x_(2)=20`