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Question 96139This question is from textbook
: When a popular brand of CD player is priced at $300 per unit, a store sells 15 units per week.Each time the price is reduced by $10, however, the sale increases by two per week. What selling price will result in weekly revenues of $7000?
Can anyone help me with this? I am not sure about the set up. 300-10x +2 = 7000?
Thanks
This question is from textbook
Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! When a popular brand of CD player is priced at $300 per unit, a store sells 15 units per week.Each time the price is reduced by $10, however, the sale increases by two per week. What selling price will result in weekly revenues of $7000?
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The relation is a linear function: y= mx+b
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You have two Points: (15,300) (17,290)
slope = [290-300]/[17-15]= -10/2 = -5
Pick a point and the slope and solve for the intercept:
300 = -5*15+b
b = 375
EQUATION:
selling price = -5*(units sold) + 375
s = -5u + 375
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Revenue = selling price * # of units
R = (-5u+375)*u
R = -5u^2+375u
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What selling price will result in weekly revenues of $7000?
7000 = -5u^2+375u
u^2-75+1400 = 0
u = [75 +- sqrt(75^2-4*1400)]/2
u = [75 +- 5]/2
u = $40 or $35
When unit price is $40 or $35 Revenue will be $7000
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Cheers,
Stan H.
Answer by scott8148(6628)  (Show Source):
You can put this solution on YOUR website! your equation is close ... for every $10 price reduction, unit sales increase by 2
(300-10x)(15+2x)=7000 ... 4500+450x-20x^2=7000 ... -2500+450x-20x^2=0
rearranging terms and dividing by -10 gives 2x^2-45x+250=0 ... factoring gives (2x-25)(x-10)=0
so x=10 and x=12.5 ... giving a selling price of 300-10(10) or $200
even though 12.5 is a solution to the equation; from the way the problem is stated, it looks like only integer values are valid
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