Question

# Scenario: You are the manager of a company that manufactures electric chainsaws. Currently the company makes...

Scenario: You are the manager of a company that manufactures electric chainsaws. Currently the company makes 5,000 chainsaws each year and sells them for \$200 each. You suspect that the company should be able to sell more chainsaws and for a higher price. However, if you raise the price too high, not as many would sell. The company also doesn’t have any storage space so if the company makes more chainsaws than they can sell, they will have to pay someone to store them. Your goal is to maximize profit, that is, the amount of money your company earns minus the amount your company spends.

It costs the company \$95 for the materials to make each chainsaw, and it costs \$400,000 each year to run the electric chainsaw factory. You conducted market research and found that at the current price of \$200 per chainsaw, the company should be able to sell 14,000 units. You also found that if the price was raised to \$220 each, the company should be able to sell 11,000 units.

1. The relative rate of change of a function at a point is the rate of change at that point divided by the value of the function at that point. Find the relative rate of change of profit.

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