u MATHEMATICAL ASSOCIATION OF AMERICA webwork math242spring-frei 7 3 optimizing

Question

u MATHEMATICAL ASSOCIATION OF AMERICA webwork math242spring-frei 7 3 optimizing functions of several variables 9 3 optimizing Functions of Several Variables Problem 9 Previous Problem List Next 2 points The telephone company is planning to introduce two new types of executive communications systems that it h to sell to ts largest commercial customers. It is estimated that if the first type of system is priced x hundred dollars p system and the second ype aty dollars per system, approximately 40 8x 5y consumers will buy the first type and buy the second type. If the cost of manufacturing the first type is $800 per system and the cost of manufacturing the second type is $3500 per system, what prices and maximize the telephone company's profit? First type: x hundred dollars per system. Second type: y hundred dollars per system. Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 2 times. Your overall recorded score is 0%. You have unlimited attempts remaining. Email instructor

Explanation / Answer

Let cost=C = 8x + 35y

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

= 40x - 8x^2 + 5xy + 50y + 9xy - 7y^2

= -8x^2 + 40x + 14xy + 50y - 7y^2

Now we know profit = sales - cost

= (-8x^2 + 40x + 14xy + 50y - 7y^2) - (8x + 35y)

= -8x^2 + 32x + 14xy + 15y - 7y^2

p/x = -16x + 14y + 32

p/y = -14y + 14x + 15

Now for optimization p/x =0 and p/y=0

16x - 14y = 32 … (1)

14x - 14y = -15 … (2)

Subtracting the (2) from (1)

2x = 47

=> x = 23.50 (100 dollars)=$ 2350

Plugging this in (2)

14(23.5) - 14y = -15

=>y = 172/7=24.57 (100 dollars)= $ 2457

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