Question 147166: I was given this problem and am not sure how to determine the answers. Could you please help?
"the production department of an electronics company projects the following costs to manufacture a new line of calculators marketing estimates the best retail price for the calculator is $92."
# of calculators cost to produce x calculators
0 $92,000
10 84,200
100 32,000
assuming this relationship is quadratic, find the quadratic function C(x)=ax^2+bx+c: I was given this problem and am not sure how to set up the quadratic formula. Could you please help?
"the production department of an electronics company projects the following costs to manufacture a new line of calculators marketing estimates the best retail price for the calculator is $92."
# of calculators cost to produce x calculators
0 $92,000
10 84,200
100 32,000
1) assuming this relationship is quadratic, find the quadratic function C(x)=ax^2+bx+c
2) how many calculators must be sold to make this line of calculators profitable (what values of x make profit positive)?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! "the production department of an electronics company projects the following costs to manufacture a new line of calculators marketing estimates the best retail price for the calculator is $92."
# of calculators cost to produce x calculators
0 $92,000
10 84,200
100 32,000
1) assuming this relationship is quadratic, find the quadratic function
C(x)=ax^2+bx+c
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I don't have a calculator with me to do it but this is what you need to do:
Substitute the "point values into the quadratic for to get three equations
in variables a, b, and c:
92000 = a*0^2 + b*0 + c
84200 = a*10^2 + b*10 + c
32000 = a*100^2 + 100b + c
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Solve this system of three equations for a, b, c
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Write the equation.
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2) how many calculators must be sold to make this line of calculators profitable (what values of x make profit positive)?
Solve ax^2 + bx + c > 0
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Cheers,
Stan H.
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