A company produces a special new type of TV The company has

A company produces a special new type of TV. The company has fixed costs of $450,000, and it costs $1500 to produce each TV. The company projects that if it charges a price of $2300 for the TV, it will be able to sell 800 TVs. If the company wants to sell 850 TVs, however, it must lower the price to $2000. Assume a linear demand. What is the maximum profit that can be reached? It is $ Round answer to nearest cent.)

Solution

Let the demand function be D = c -bp where D is the quantity demanded, c is the other demand affecting factors ,p is the price and b is the slope of the demand curve. Then, 800 = c-2300b...(1) and 850 = c -2000b…(2). On subtracting the 1^st equation from the 2^nd equation, we get 850-800 = c -2000b-c +2300b or, 50= 300b so that b = 50/300 = 1/6. On substituting b = 1/6 in the 2^nd equation, we get 850 = c- 2000/6 so that c = 850+2000/6 = 850+1000/3 = 3550/3. Then D= 3550/3 –(1/6)p.