SOLUTION: The total cost (in dollars) for a company to produce X items per week is C equals 70 X +300. The revenue for selling all X items is our equals 110X -0.5 X squared. How many items m
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-> SOLUTION: The total cost (in dollars) for a company to produce X items per week is C equals 70 X +300. The revenue for selling all X items is our equals 110X -0.5 X squared. How many items m
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Question 1180677: The total cost (in dollars) for a company to produce X items per week is C equals 70 X +300. The revenue for selling all X items is our equals 110X -0.5 X squared. How many items must it produce and sell each week for its weekly profit to be $300. Answer by greenestamps(13200) (Show Source):
Revenue is 110x-0.5x^2; cost is 70x+300; you want the profit to be 300:
Simplify and combine like terms on the right
Get everything on one side of the equation with a positive coefficient on the x^2 term
Multiply by 2 to clear fractions to make the quadratic easier to factor
Factor the quadratic; this one factors nicely
ANSWER: A profit of $300 can be obtained by producing and selling EITHER 20 units or 60 units.
