another calculus question (functions)

**izaiyoi** · January 21st 2008, 07:33 AM

costs associated with manufacturing x products is described by:
C(x)=x^3-7x^2+18x+110
revenue for this level of manufacturing is : V(x)=3x^3-21x^2+84x+180

Profit = V(x)-C(x)
Calculate
1. expression for profit associated with manufacturing x items
2. how many items should be manufactured to minimise production costs
3. how many items need to be manufactured to maximise the profit

**Soroban** · January 21st 2008, 07:57 AM

Hello, izaiyoi!

This is very straight foward . . . Exactly where is your difficulty?

Costs associated with manufacturing x products is described by:
. . $C(x)\:=\:x^3-7x^2+18x+110$

Revenue for this level of manufacturing is: . $V(x)\:=\:3x^3-21x^2+84x+180$

$\text{Profit }\:= \:P(x)\:=\:V(x)-C(x)$

Calculate:
1. Expression for profit associated with manufacturing $x$ items

They told us that: . $P(x) \:=\:V(x)-C(x)$ . . . didn't they?

$\text{So: }\;P(x) \;=\;\underbrace{\bigg[3x^3-21x^2+84x+180\bigg]}_{v(x)} - \underbrace{\bigg[x^3-7x^2+18x + 110\bigg]}_{C(X)} \;=\;\; ? ?$

2. How many items should be manufactured to minimise production costs?