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.
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So my answer was $5.70, but the actual answer was something like $1.70.
My formula, to find the profit equation, is P(x)=R(x)-C(x), which was 4.5x-0.0001x^2+2x+3200.
The derivative was P'(x)=-0.0002x+6.5 (according to my work, not sure). I then subbed in 4000 into that equation.
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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
Ok. Give me a second, I need a drink of water.
Ok. thank you. I figured it out with your assistance.