Let <span>the production level that will yield a maximum profit for the manufacturer be x.
</span>The unit price of the disc is given by p = -0.0006x^2 + 65.
The revenue from selling x discs (R(x)) = px = -0.0006x^3 + 65x
Profit = Revenue - Cost = -0.0006x^3 + 65x - (-0.002x^2 + 13x + 4000) = -0.0006x^3 + 0.002x^2 + 52x - 4000
For maximum profit, dP/dx = 0
-0.0018x^2 + 0.004x + 52 = 0
Using quadratic formular, x = 171
Therefore, <span>the production level that will yield a maximum profit for the manufacturer is 171 discs.</span>
X = 6, y = 8, z = 3
3(8) + (6)² = 24 + 36 = 60
= 20
Answer: The three consecutive odd integers are: -15, -13, and -11 .
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Explanation:
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x + (x + 2) + (x + 4) = -39 ;
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in which "x" is one of the integers,
"(x + 2)" is the next consecutive odd integer;
"(x + 4)" is the third consecutive odd integer.
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By solving for "x", we can solve for each of three (3) consecutive odd integers.
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x + (x + 2) + (x + 4) = -39 ;
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1x + 1x + 2 + 1x+ 4 = -39 ;
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3x + 6 = -39 ;
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Subtract "6" from EACH side of the equation:
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3x + 6 − 6 = -39 <span>− 6 ;
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to get: 3x = -45 ;
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Divide EACH side of the equation by "3" ;
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3x / 3 = -45 / 3 ;
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to get: x = -15 ;
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x + 2 = -15 + 2 = -13 ;
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x + 4 = -15 + 4 = -11 .
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Are: -15, -13, and -11 ; Consecutive odd integers? YES!
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Does: -15 + (-13) + (-11) =? = -39 ??
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-15 </span>− 13 <span>− 11 = ? 39 ?? YES!
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Answer: The three consecutive odd integers are: -15, -13, and -11.
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Start with 7-4=3
Then 3x3=9
Then 18+9=27
Answer 27
