Zenith Linear
March 2nd, 2010
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Zenith Linear
Errr... having trouble understanding these 2 word problems? Please help!?
1.) Radiation King Inc. sells microwave ovens for $300 each. At that price, RKI can sell 200 ovens each week. If RKI lowers the price/ oven to $250 sales increase to 225 ovens each week. Find the price function p assuming that p is linear. What price should be set if RKI decides they need to sell only 125 ovens each week?
2.) Zoom Bus Lines provides transportation between Zenith and Mohalis. Each week that Zoom charged $16/ticket, 2000 tickets were sold. After lowering the price to $12/ticket, sales increased to 24000 tickets/week. Find the price function p assuming that p is linear. How many tickets can Zoom sell each week if the price is set at 15.000/ticket? If Zoom wants to sell exactly 1500 tickets each week, what price should be set?
Also if you're a mathematician do you mind if I e-mail you because I don't do very well in math and I want to do well on the test I have this Tuesday
Assuming the relationship is linear means that the function is a line like y = mx +b
But for this exercise
price = m units sold + B
You are given two points on the line (200.300) and (225,250)
m = change in price / change in units sold
m = - 50 / 25 = -2
b = price if 0 units sold = 300 - 200 x m = 300 - -400 = 700
so the formula for the line is:
price = -2 units sold + 700
Sustitiute in 125 to get the price to sell 125 units.
price = -2 ( 125) + 700 = 450
In the second case given points (2000,16) and (2400,12)
m = -4/400 = -0.01
B = 16 - 2000 m = 16 - 2000 x - 0.01 = 16 + 20 = 36
price = -0.01 units sold + 36
a, ) 15 = -0.01 units sold + 36
units sold = -21 x 100 = 2100
b.) price = -0.01 x 1500 + 36 = 36 -15 = 21
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