Problema Solution
The demand equation for a microwave is p=140-0.0001x, where p is the unite price in dollars of the microwave and x is the number of unites produced and sold. The cost equation for the microwaves is C=80x+150,000, where C is the total cost in dollars and x is the number of units produced. The total profit obtained by producing and selling x units is given by P=R-C=xp-C. You are working in the marketing department of the company that produces microwaves, and you are asked to determine a price p that would yield a profit of $9 million. Is this Possible? Explain.
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R=xp-C.
=x(140-0.0001x)-(80x+15000).
140x-0.0001x^2-80x-150,000.
R(x)=60x-0.0001x^2150,000.
9*10^6=60x-0.0001x^2-150000.
0.0001x^2-60x+9150000=0.
It is a quadartic equation.
The discrininate D=b^2-4ac=(-60)^2-4*0.0001*9150000
=-60<0.
No real roots.
Hence a profit of $9 million is not possible.