**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.**

Continue reading Business Calculus Word Problem

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