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8090 [49]
2 years ago
9

The expense function for a widget is E = -3,000p + 250,000. The revenue function is R = -600p^2 + 25,000p. Write the profit equa

tion in simplified form ( P= R- E) . Use the axis of symmetry formula to determine the maximum profit price and the maximum profit.
Mathematics
1 answer:
erastova [34]2 years ago
4 0

The maximum profit price and maximum profit are 23.33 and  301666.66 respectively

<h3>Difference of functions</h3>

Given the following functions

Expense =  E = -3,000p + 250,000.

The revenue function is R = -600p^2 + 25,000p

The profit is the difference between the revenue and cost to have;

P = R - E

P = -600p^2 + 25,000p - ( -3,000p + 250,000.)

Simplify

P = -600p^2 + 25,000p - ( -3,000p + 250,000.)

P = -600p^2 + 25,000p +3,000p-  250,000

P = -600p^2  + 28000p - 250000

The maximum price occurs when P'(p) = 0

P'(p) = -1200p + 28000

0 = -1200p + 28000

p = 28000/1200
p = 23.33

Substitute

P(23.33) = -600(23.33)^2  + 28000(23.33) - 250000

P(23.33) = -326573.34 - 250000 + 653240

P(23.33) = 301666.66

Hence the maximum profit price and maximum profit are 23.33 and  301666.66 respectively

Learn more on maximum function here: brainly.com/question/82347

#SPJ1

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Answer:

The value of m is 6.

Step-by-step explanation:

Here, the given equation,

x^4-(3m+2)x^2+m^2=0

x^4+0x^3-(3m+2)x^2+0x+m^2=0

Let the roots of the equation are a-3b, a-b, a+b and a + 3b, ( they must be form an AP )

Thus, we can write,

a-3b+a-b+a+b+a+3b=\frac{\text{coefficient of }x^3}{\text{coefficient of }x^4}

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\implies a=0----(1)

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19m^2-108m-36=0

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(19m+6)(m-6)=0

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Hence, the value of m is 6.

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3 years ago
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Answer:

x=2

Step-by-step explanation:

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