Polynomials II

A bakery sells 3,000 cupcakes each month at $4 per cupcake. The owner wants to know how increasing the price might affect the bakery’s monthly revenue. Here, revenue is the total amount of money earned from sales.

Suppose the owner increases the price of each cupcake by x dollars. The new price is four plus x dollars.

A market study shows that for every $1 increase in price, monthly sales decrease by 50 cupcakes. So, an increase of x dollars reduces monthly sales by 50x cupcakes. The new monthly sales are 3,000 minus 50x.

To find the monthly revenue, the owner multiplies the new price by the new monthly sales. This gives revenue as the product of four plus x and three thousand minus fifty x.

Using the distributive property, each term in the first polynomial is multiplied by each term in the second polynomial. Then, the like terms are combined to form a quadratic polynomial.

This quadratic polynomial models the bakery’s monthly revenue when the price of each cupcake increases by x dollars.