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A clothing business finds there is a linear relationship between the number of shirts, Q ,it can sell and the price, P , it can charge per shirt. In particular, historical data shows that 4000 shirts can be sold at a price of $ 133 , while 27000 shirts can be sold at a price of $ 41 . Give a linear equation in the form P = a Q + b that gives the price P they can charge for Q shirts. (This is called a demand function.)

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Answer:

P = -0.004Q + 149

Step-by-step explanation:

The general form of the linear equation is:

[tex]P=aQ+b[/tex]

The slope of the equation (a) can be found by using the two given points (4,000; $133) and (27,000; $41)

[tex]a = \frac{\$41-\$133}{27,000-4,000}\\a=-0.004[/tex]

Applying the point (4,000; $133) to the equation below yields in the linear equation for Price as a function of the number of shirts:

[tex]P-P_0=a(Q-Q_0)\\P-133=-0.004(Q-4,000)\\P = -0.004Q+149[/tex]

The linear equation is:

P = -0.004Q + 149

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