Math Algebra 2

Ok im stumped on this HW problem can anyone help?
The Blue clothing company makes both shirts and pants. Each shirt gives a profit of \$25, while a pair of pants yields \$55. Both shirts and pants are made using machines and human labor. A single shirt takes an hour of machine labor and an hour of human labor. A pair of pants requires 3 hours of machine labor and 2 hours of human labor. Each day the company can devote a total of 160 hours of human labor and 200 of machine labor. The company must make at least 15 pairs of pants every day, but never has enough material to make more than 70. The number of shirts made in a day can not exceed 100. Lastly, the number of pants made in a day can never be more than the number of shirts. How many pants and shirts should the company make in a day to maximize profits? What is the maximum profit?

So far i set up the profit equation 25x+55y=Profit and now im stuck on the different restrictions for it i think i have y≤70 x≤100 plz help!

1. 👍 0
2. 👎 0
3. 👁 51
1. human hrs = 160, or 2x+6y=160
machine hrs = 200, or 2x+9y=200
minimum of 15 pants, or y>=15
must make more shirts than pants, or
x>=y
the maximum profit is where the equation 25x+55y=profit has a local maximum. One way to determine this is using the 1st derivative and set this equal to zero.

1. 👍 0
2. 👎 0
posted by FredR
2. hey thanks alot for all that help i graphed it on some paper and in my calculator and i think for the answer i got 18.18 for x and 18.18 for y and the profit would be \$1454.54 can anyone confirm if this is correct? thanks
x=shirt y=pants

1. 👍 0
2. 👎 0
posted by John
3. i got 18.18 for x and 18.18 for y and the profit would be \$1454.54 does that look like its right?

1. 👍 0
2. 👎 0
posted by John
4. I got a maximum profit of \$4200 with 40 pants and 80 shirts.

1. 👍 0
2. 👎 0
posted by FredR

Similar Questions

1. Civics ASAP PLZ =:)

Of the businesses or individuals in the list below, who would benefit most from a weak U.S. dollar? • A family from France planning to vacation in the U.S. • A Japanese company that makes electronics to sell in the U.S. • An

asked by Anonymous on May 30, 2015
2. College Econ

There are two types of people. Red's and Blue's. In a given week, Red's can make 5 pieces of clothing or kill 10 buffalo (and all linear combo in between) In a given week, Blue's can make 12 pieces of clothing or kill 4 buffalo

asked by Nichole on August 27, 2009
3. Math

Whats the solution of 2(h−8)−h=h−16? This has me stumped, can you also explain how to do this problem, so i can use that if i get stumped on another question?

asked by Clorox on September 20, 2018

Jones Manufacturing sent Blue Company an invoice for equipment with a list price of \$10,000. The invoice is dated July 27 with terms of 2/10, EOM. Blue Company is entitled to a 40% trade discount. If the invoice is paid on

asked by Jeffrey W on December 2, 2014
5. History

I am totally stumped. The picture we are to look at is called Five generations of slaves in South Carolina. The picture shows a family outside their home. The questions we are asked is to 1-make inferences about the owner of the

asked by m on March 16, 2011
6. Chemistry

Hi. Can anybody help me with crystals? I have a gas that makes blue crystals when it's been hold in low temperature and high pressure. If pressure becomes higher, it makes red crystals, if pressure becomes lower then it reurns to

asked by Ksenija on March 21, 2009
7. Science

I have a science project du and im trying to look for a problem on why the sky is blue. I know that why the sky is blue is a question but i cant find the actuall "problem" The sky is blue because of Rayleigh scattering. I know of

asked by Jack on March 7, 2007

Is the subject line "Improving Customer Service" appropriate in a message to superiors? A. Yes, because it focuses on solving the problem. B. No, because the word "service" makes the subject line seem negative. C. No, because the

asked by Rain Misoa on August 15, 2010
9. Math

A website developer is designing a website for a clothing company. Clothing items will be arranged on a web page in a rectangular display showing 32 clothing items, with the same number of items in each row. How many ways can the

asked by OConnor on December 14, 2014
10. Civics.

Which of the following businesses would prefer a strong U.S. dollar to a weak one? A U.S. company that exports cars to Mexico A French company that imports clothing from the United States A U.S. company that imports bananas from

asked by Ginger V. on July 21, 2016

More Similar Questions