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Linear Functions

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1. A company sells it's products in a market where the market price, p, is linked to the quantity sold, q, by the linear equation p=120-2q.

a) Calculate the market price if the company sells 50 units. What is the revenue equation and the revenue if company sells 50 units?

The company incurs fixed costs of $400 and an additional cost of $12 for each unit produced.

b) What is the cost equation? How much will it cost to produce 50 units?

c) What is the profit equation? What profit will the company make from producing and selling 50 units?

d) Calculate the number of units that will maximize the profit. What is the corresponding market price that will maximize profit? What is the maximum profit?

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The expert provides linear functions for market price, and cost equation.

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1a) We know p = 120 - 2q, so if the company sells 50 units, p = 120 - 2(50) = 20.

Revenue = price per unit X number of units sold = 20 X 50 = 1000.

b) Cost = fixed cost + per unit cost X number of unit ...

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