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Dennis_Churaev [7]
3 years ago
11

The Cool Company determines that the supply function for its basic air conditioning unit is S(p) = 40 + 0.008p3 and that its dem

and function is D(p) = 200 - 0.16p2, where p is the price. Determine the price for which the supply equals the demand.
Mathematics
1 answer:
myrzilka [38]3 years ago
3 0

We are given the functions:

<span>S (p) = 40 + 0.008 p^3                                     ---> 1</span>

<span>D (p) = 200 – 0.16 p^2                                     ---> 2</span>

 

T o find for the price in which the price of supply equals demand, all we have to do is to equate the two equations, equation 1 and 2, and calculate for the value of p, therefore:

S (p) = D (p)

40 + 0.008 p^3 = 200 – 0.16 p^2

0.008 p^3 + 0.16 p^2 = 160

p^3 + 20 p^2 = 20,000

p^3 + 20 p^2 – 20,000 = 0

Calculating for the roots using the calculator gives us:

p = 21.86, -20.93±21.84i

 

Since price cannot be imaginary therefore:

p = 21.86

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