Question 110194: I am having a difficult time setting this problem up, please help!
Let X be the units sold,P is the price per unit, and R be the total revenue. If R = XP, and the demand equation for the the product is P = 60-0.0004 X. How many units must be sold to produce revenue of $220,000 ?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Let X be the units sold,
:
P is the price per unit,
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R be the total revenue.
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If R = XP, and the demand equation for the the product is P = 60-0.0004X.
:
R = XP
Substitute (60-.0004X) for P (from the above equation)
R = X*(60-.0004X)
:
R = 60X - .0004X^2
or
-.0004X^2 + 60X = R
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It says,"How many units must be sold to produce revenue of $220,000 ?"
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Substitute 220000 for R in the above equation:
:
-.0004X^2 + 60X = 220000
:
-.0004X^2 + 60X - 220000 = 0; a quadratic equation
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Solve this for x using the quadratic formula, positive solution:
x = 146,239 (rounded) units sold to make $220,000
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