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A large department store is prepared to buy 3,800 of your tie-dye shower curtains per month for $6 each, but only 3,550 shower curtains per month for $11 each. What is the linear demand function for your tie-dye shower curtains?q(p) =

Question

A large department store is prepared to buy 3,800 of your tie-dye shower curtains per month for 6each,butonly3,550showercurtainspermonthfor6 each, but only 3,550 shower curtains per month for 11 each. What is the linear demand function for your tie-dye shower curtains?q(p) =

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Solution

The linear demand function, q(p), can be found using the formula for the slope of a line (m = (y2 - y1) / (x2 - x1)) and the formula for a line (y = mx + b).

First, we need to find the slope (m) of the line. We have two points given in the problem: (p1, q1) = (6, 3800) and (p2, q2) = (11, 3550).

So, m = (q2 - q1) / (p2 - p1) = (3550 - 3800) / (11 - 6) = -250 / 5 = -50.

Next, we substitute one of the points and the slope into the line equation to find b. Let's use the point (6, 3800):

3800 = -50 * 6 + b 3800 = -300 + b b = 4100

So, the linear demand function is q(p) = -50p + 4100.

This problem has been solved

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