A furniture company sells 3000 chairs per week at a price of $150 apiece; when the price is lowered to $125, the company sells 3500 chairs per week. If the company wishes to liquidate its entire remaining inventory of 4250 chairs in the next week, what price should they seek?

Question

A furniture company sells 3000 chairs per week at a price of $150 apiece; when the price is lowered to $125, the company sells 3500 chairs per week.  If the company wishes to liquidate its entire remaining inventory of 4250 chairs in the next week, what price should they seek?

anonymous · Answer

First, find the an equation that expresses this situation.  Let's assume this relationship is a linear one.  The independent variable (x) is the price of the chair and the dependent variable is the number of units sold.

Find the slope, which is the change in y divided by the change in x, or
$$m=\frac{y_2-y_1}{x_2-x_1}$$$$m=\frac{3500-3000}{125-150}=-20$$
Put this into the slope-intercept equation:
$$y=mx+b$$$$y=-20x+b$$
Choose one of the points (150, 3000) or (125, 3500).  Let's use the first point, (150, 3000).  In this point, 150 is the x-coordinate, so we will substitute 150 for x.  3000 is the y-coordinate, so we will substitute 3000 for y.
$$3000=-20(150)+b$$Solve for b:

$$3000=-3000+b$$$$b=6000$$So our equation is now
$$y=-20x+6000$$
The question asks how much should be charged in order to sell 4250 chairs, so we substitute that for y and solve for x:
$$4250=-20x+6000$$$$-1750=-20x$$$$x=87.5$$So the vendor should sell each chair for $87.50

anonymous · Answer

wow that is not what I was expecting

anonymous · Answer

Hey Can SomeOne Help Me After This One :D http://openstudy.com/groups/mathematics#/groups/mathematics/updates/4e24e52b0b8b3d38d3b761da