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 y hundred 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 $1300 per system and the cost of manufacturing the second type is $2100 per system, what prices x and y will maximize the telephone company's profit?

Explanation / Answer

profit on first item =(40-8x+5y)x -1300 ,profit on second item =(50+9x-7y)y-2100 ,netprofit =(40-8x+5y)x -1300+(50+9x-7y)y-2100 =40x-8x^2 +14xy-7y^2+50y-3400 ,At least zero items will be sold,but less than zero products cannot be sold,hence applying the condition 40-8x+5y>=0 gives 8x-5y=0 gives 7y-9x

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