Question

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.)

Answer 1

P = -0.004Q + 149

Explanation:

The general form of the linear equation is:

`P=aQ+b`

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

`a = (\$41-\$133)/(27,000-4,000)\\a=-0.004`

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:

`P-P_0=a(Q-Q_0)\\P-133=-0.004(Q-4,000)\\P = -0.004Q+149`

The linear equation is:

P = -0.004Q + 149