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Marginal Cost, Revenue and Profit

Q:  Word problem, here it is:

(a) The marginal cost function for Janes Coffee Co is MC(q) = 40 – 2q, where q is the number of tons of coffee produced.  Fixed costs are $250.  The marginal revenue function is MR(q) = 100 – 4q.  What is the value of the profit function P(q) when q = 20?

(b) The average cost when q=20 is?

(c) The change in revenue if sales increase from 10 to 15 tons is?

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Business Calculus Word Problem

BACKGROUND

First we need some basics (assuming everything is linear, we continue):

We logically know that:

Profit = What you make – What you spend

In math, that is:

P = Revenue – Cost

(1) P = R – C

And,

Revenue = price * quantity

(2) R = px

(3) Cost = (variable cost)*x + (fixed cost)

Now, there is a difference between big P (profit) and little p (price or demand)

We usually assume price is linear, so:

(4) p = mx + b

Everything in BOLD are things you must know!

OK…. Now let’s start deciphering the actual problem:

Q:  A manufacturer sells 150 tables a month at the price of $200 each. For each $1 decrease in price, he can sell 25 more tables. The tables cost $125 to make. Express monthly profit as a function of the price, draw a graph and estimate the optimal selling price.

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