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?
Continue reading Marginal Cost, Revenue and Profit
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
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.
Continue reading Business Calculus Word Problem