Question 303147: Supply and Demand. The supply and demand for the sale of stereos by Sound Ideas are given by S(x)=e^x and D(x)=162,755e^-x, where S(x) is the price at which the company is willing to supply x stereos and D(x) is the demand price for a quantity of x stereos. Find the equilibrium point.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Supply and Demand. The supply and demand for the sale of stereos by Sound Ideas are given by S(x)=e^x and D(x)=162,755e^-x, where S(x) is the price at which the company is willing to supply x stereos and D(x) is the demand price for a quantity of x stereos. Find the equilibrium point.
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Equilibrium occurs when Revenue = Cost.
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Solve : e^x = 162,755e^-x
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Multiply both sides by e^x to get:
e^(2x) = 162755
Take the natural log and solve for "x":
2x = ln(162755)
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x = 6
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Find the equilibrium point.
e^x = e^6 = 403.43
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Cheers,
Stan H.
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