Economists frequently use linear functions to construct models for the relationship between price and demand for a small business. Generally, we consider the selling price p of the item to be a linear function of the demand x (the number of units consumers will purchase). Pomelia has begun a home business making decorative lawn sprinklers out of copper tubing. She has found that she can sell 20 sprinklers per month if they are priced at $60 each but only 12 sprinklers per month if they are priced at $70.
a. Find a linear function p(x) giving the price of the sprinklers as a function of the number sold.
b. How many sprinklers will she sell if the sprinklers are priced at $55?
c. If Pomelia wants to sell at least 30 sprinklers per month, what price should she charge?
d. Explain what the intercepts of the line mean in this situation.
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