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 $1500 per system and the cost of manufacturing the second type is $2600 per system, what prices x and y will maximize the telephone company's profit?

First type: x = hundred dollars per system.

Second type: y = hundred dollars per system.

Explanation / Answer

Profit = sales -cost

cost = 1500x + 2600y

sales = (50+9x-7y)*y+ (40-8x+5y)*x

So P = 40x-8x^2+5xy + 50y+9xy-7y^2 -1500x-2600y

Take partials wrt to x and y and set = 0.

Px = 40 -16x +5y +9y -1500 = 0

Py = 5x + 50 +9x -14y-2600 = 0

Get two equation in 2 unknowns

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