Question

MATICAL ASSOCIATION OF AMERICA NU Kwebwork / math242winter-hulbert / week 3b-7.3 optimizing functions.of several variables /7 Logged in as dmcclos Sets Week 3b 7 3 Optimizing Functions of Several Variables: Proble -73 ing ns of Variables PreviousProblem List Next em 7 (2 points) 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 gs buy the second type. If the cost of manufacturing the first type is $1200 per system and the cost of manufacturing the second type is $3400 per system, what prices x and y will maximize the telephone company's profit? y consumers will blems First type: x hundred dollars per system Second type: y- 2 v hundred dollars per system. Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempled this problem 0 times. You have unlimited attempts remaining Email instructor MacBook Pro

Answer 1

We have cost = 12x+34y

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

= 40x-8x²+5xy+50y+9xy-7y²

⁼ -8x^​2​​+40x+14xy+50y-7y²

profit = sales - cost

= (-8x^{​​​​2}​​​+40x+14xy+50y-7y² )-(12x+34y)

-8x^{​​​​2}​​​+28x+14xy+16y-7y2

d/dx = -16x+14y+28

d/dy = -14x+14y+16

Setting them to 0

16x-14y = 28........(1)

14x-14y. = -16.........(2)

Solving (2) from (1)

2x = 44

X = 22 (100 dollars)

Putting this value in (2)

14(22)-14y= -16

y = 324/14 = 23.14 (100 dollars)