A cable TV company has 4800 customers paying $110 each month. If each $1 reduction in price attracts 50 new customers, find the price that yields maxi

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Kaz_90

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A cable TV company has 4800 customers paying $110 each month. If each $1 reduction in price attracts 50 new customers, find the price that yields maximum revenue.
 
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Kaz_90 said:
A cable TV company has 4800 customers paying $110 each month. If each $1 reduction in price attracts 50 new customers, find the price that yields maximum revenue.
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Let P be the price that gives C customers. Write the relation as "C= aP+ b". When P= 110, C= 4800 so 4800= a(110)+ b. If P= 109, a $1 reduction from $110, there will be 4800+ 50= 4850 so a(109)+ b= 4850. Solve those two equations for a and b.

The "revenue" is the amount each customer pays times the number of customers: PC= P(aP+ b)= aP^2+ bP with the a and b you just found.

Now what methods you know for maximizing a function? That is a quadratic equation in P so you could "complete the square" in order to find the vertex. Or, if you have taken Calculus, you could differentiate with respect to P, set the derivative to 0, and solve that for P,
 
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