The telephone company is planning to introduce two new types of executive commun

Question

The telephone company is planning to introduce two new types of executive communications systems that it hopes to sell to its largest commercial customers. It is estimated that if the first type of system is priced at x hundred dollars per system and the second type at yhundred dollars per system, approximately 40?8x+5y consumers will buy the first type and 50+9x?7y will buy the second type. If the cost of manufacturing the first type is $600 per system and the cost of manufacturing the second type is $2300 per system, what prices xand y will maximize the telephone company's profit?

First type: x = ______ hundred dollars per system.

Second type: y = ______ hundred dollars per system.

Explanation / Answer

Income from 1st system = 100x (40?8x+5y)
Income from 2nd system = 100y (50+9x?7y)
Cost for 1st system = 600 (40?8x+5y)
Cost for 2nd system = 2700 (50+9x?7y)

Profit from 1st system = (100x?600) (40?8x+5y)
Profit from 2nd system = (100y?2700) (50+9x?7y)

Profit =
F(x,y) = (100x?600) (40?8x+5y) + (100y?2700) (50+9x?7y)
........ = ?800x

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