A sporting goods store has ordered tents that cost $110 each. The shipping for the entire order is $200. The store can sell the tents for $230 each...

Question

A sporting goods store has ordered tents that cost $110 each. The shipping for the entire order is $200. The store can sell the tents for $230 each. Find the formula for the profit function in terms of x where xis the number of tents ordered.

Answer 1

Profit is the difference between income and expenses

P = I - E

The income the money earned, in this case the amount that the store receives when it sells the tent. Since each tent sells for $230, the income is that price times the number of tents sold, which the problem calls "x". We can represent the income with the following equation:

I = $230 (x)

The expense is the total amount of money that the store had to be able to sell the tent. Since is costs the store $110 to purchase a tent, purchasing "x" tents would cost $110(x). It also cost $200 to ship any order, so the total expense can be represented by:

E = $110(x) + $200

We can now substitute our equation for income and our equation for expenses into our profit equation:

P = [$230 (x)] - [$110(x) + $200]

Simplifying this equation gives us:

P = $120(x) + $200