Question

a company sells running shoes. if the price of a pair of shoes in dollars is p, the company estimates that it will sell 50,000 - 400p pairs of shoes. write an expression that represents the revenue in dollars from selling running shoes if a pair of shoes is priced at p dollars.

Explanation:

Step1: Recall revenue formula

Revenue is calculated as the product of price per unit and the number of units sold. So, Revenue \( R = \text{Price} \times \text{Quantity} \).

Step2: Identify price and quantity

The price per pair of shoes is \( p \) dollars, and the quantity of shoes sold is \( 50000 - 400p \) pairs.

Step3: Multiply price and quantity

To find the revenue, we multiply the price \( p \) by the quantity \( 50000 - 400p \). Using the distributive property (also known as the FOIL method for binomials, here we distribute \( p \) over the terms in the quantity), we get:
\( R = p\times(50000 - 400p) = 50000p - 400p^{2} \)

Answer:

The expression for revenue is \( 50000p - 400p^{2} \) (or equivalently \( - 400p^{2}+50000p \))