A yogurt company estimates that the revenue from selling x containers of yogurt is 4.5x. Its cost, C, in dollars, for producing this # of containers of yogurt is C(s)=0.0001x^2+2x+3200. Determine the marginal profit from selling 4000 containers of yogurt.

Question

istim · Answer

So my answer was $5.70, but the actual answer was something like $1.70.

istim · Answer

My formula, to find the profit equation, is P(x)=R(x)-C(x), which was 4.5x-0.0001x^2+2x+3200.

istim · Answer

The derivative was P'(x)=-0.0002x+6.5 (according to my work, not sure). I then subbed in 4000 into that equation.

anonymous · Answer

I think the error made is when u calculate marginal profits from total profits. Don't think it work that way. Marginal profits must be calculated from marginal cost and marginal revenue. 

So i went ahead to differentiate total cost, 

Marginal Cost, MC = 0.0002x+2 
Substitute x= 4000, MC= 0.0002(4000)+2 = 2.8

Differentiating total revenue,
marginal revenue, MR = 4.5

Marginal Profits = Marginal Revenue - Marginal Cost
= 4.5 - 2.8
=1.7

istim · Answer

Ok. Give me a second, I need a drink of water.

istim · Answer

Ok. thank you. I figured it out with your assistance.

anonymous · Answer

np. Glad to be of help.