SOLUTION: The demand equation for a microwave is p = 140 � 0.001x where p is the unit price in dollars and x is the number of units produced and sold. The cost equation for the microwave is

Question 1026350: The demand equation for a microwave is p = 140 � 0.001x where p is the unit price in dollars and x is the number of units produced and sold. The cost equation for the microwave is C = 40x + 150,000 where C is the total cost in dollars and x is the number of units produced. The total profit P obtained by producing and selling x units is given by P = R � C = xp � C. Is there a price p that yields a profit of $3 million? Explain your answer.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The demand equation for a microwave is p = 140 � 0.001x where p is the unit price in dollars and x is the number of units produced and sold.
The cost equation for the microwave is C = 40x + 150,000 where C is the total cost in dollars and x is the number of units produced.
The total profit P obtained by producing and selling x units is given by P = R � C = xp � C. Is there a price p that yields a profit of $3 million?
:
Revenue (px) - cost = 3 million
x(140-.001x) - (40x + 150000) = 3,000,000
140x - .001x^2 - 40x - 150000 = 3000000
-.001x^2 + 140x - 40x = 3000000 + 150000
-.001x^2 + 100x - 3150000 = 0
This is a quadratic equation, find x that gives us the maximum
x = -b/(2a) where b=100 and a = -.001
x =
x = 50000 units for max profit
Find the actual profit when 50000 are made
-.001(50000^2) + 100(50000) = $2,500,000 is max profit; the answer is no.
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