Question

large department store is prepared to buy 3,800 of your tie-dye shower curtains per month for $5 each, but only 3,500 per month for $10 each. What is the linear demand function for your tie-dye shower curtains?

Answer 1

The linear demand function for the tie-dye shower curtains, based on the given price-quantity pairs, is P = -$1/60Q + $68.33.

Step-by-step explanation:

The question is asking to find the linear demand function for tie-dye shower curtains based on two different price-quantity scenarios provided by a large department store. To construct a demand function, we need two points that will help us determine the slope of the demand curve.

The first point (P1, Q1) is ($5, 3800) since the store is willing to buy 3800 curtains at $5 each. The second point (P2, Q2) is ($10, 3500), with 3500 curtains at $10 each. The demand function can be written in slope-intercept form: P = mQ + b, where P is the price, Q is the quantity, m is the slope, and b is the y-intercept.

To find the slope (m), we use the formula m = (P2 - P1) / (Q2 - Q1). Here, m = ($10 - $5) / (3500 - 3800) = $5 / (-300) = -$1/60.

To find the y-intercept (b), we use one of the given points and the slope just calculated. Let's use point (P1, Q1): $5 = (-$1/60)(3800) + b. Solving for b gives us b = $5 + $1/60 * 3800 = $5 + $63.33 = $68.33.

So, the demand function for the tie-dye shower curtains is: P = -$1/60Q + $68.33.