Question

The middle school band is selling spirit mugs to raise money for new instruments. It costs them $3 for each mug with the school logo on it and they have to pay $100 to get the mugs delivered. They plan to sell the mugs for $10. Create a function to represent the profit the students will make from selling x mugs.

Answer 1

The profit function that represents the money made from selling x spirit mugs is P(x) = 7x - 100, considering the production and delivery costs against the selling price.

Step-by-step explanation:

The function to represent the profit the students will make from selling x spirit mugs can be constructed by considering the cost to produce and deliver the mugs against the selling price. The total cost for producing x mugs is the sum of the production costs ($3 per mug) and the fixed delivery cost ($100). Therefore, the total cost function is C(x) = 3x + 100. They plan to sell the mugs for $10 each. Thus, the revenue function is R(x) = 10x. To find the profit function, we subtract the total costs from the revenue, yielding P(x) = R(x) - C(x) = 10x - (3x + 100) which simplifies to P(x) = 7x - 100.

To determine the profit the students will make from selling x mugs, we need to subtract the total costs from the total revenue. The total costs include the cost per mug with the school logo and the delivery cost. The total revenue is the price per mug multiplied by the number of mugs sold. Let's create a function to represent this:

Profit = (Price per mug * Number of mugs sold) - (Cost per mug * Number of mugs sold + Delivery cost)

Profits(x) = (10 * x) - (3 * x + 100)

Where x represents the number of mugs sold.