Question 109284: greatly appreciate your help on this question - thank you
Determine the revenue function: a company has found that if they produce x units of a product, they must sell them each at $10 - 0.2x if they are to sell them all.
would revenue function be R(x) = P*q = (10 - 0.2x)*x
and also, their fixed costs are $40 and their Variable costs per unit are $1 Determine the cost and profit functions
Functions are cost = 1(x) + 40 ?
Profit function = total revenue - total cost
= -0.2x^2 + 9x + 40 ?
Am I at all close?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Determine the revenue function: a company has found that if they produce x units of a product, they must sell them each at $10 - 0.2x if they are to sell them all.
would revenue function be R(x) = P*q = (10 - 0.2x)*x
Yes, that is correct for the Revenue equation.
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and also, their fixed costs are $40 and their Variable costs per unit are $1 Determine the cost and profit functions
Functions are cost = 1(x) + 40 ?
Yes, that is correct for the Cost equation.
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Profit function = total revenue - total cost
10x-0.2x^2 = x+40
-0.2x^2+9x-40=0
Rearrange:
0.2x^2-9x+40=0
Multiply thru by 5 to get rid of the decimal:
x^2 - 45x + 200 = 0
x = [45 +- sqrt(45^2-4*200)]/2
x = [45 +- 35]/2
x = 40 or x = 5
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Cheers,
Stan H.
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