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Question
A paint supplier has two machines that produce both indoor and outdoor paint. To meet one contractual obligation,
the company must produce at least 60 gallons of indoor paint and 100 gallons of outdoor paint.
Machine I makes 3 gallons of indoor paint and 10 gallons of outdoor paint per hour.
Machine II makes 4 gallons of indoor paint and 5 gallons of outdoor paint per hour.
It costs $28 per hour to run Machine I and $33 per hour to run Machine II.
List the Constraints and determine the minimum cost.
Facts
We need 60 gallons of indoor paint and 100 gallons of outdoor paint
MI) Produces 3 indoor, 10 outdoor per hour at $28/hour, called x
MII) Produces 4 indoor, 5 outdoor per hour at $33/hour, called y
Z Row
-28 -33
Constraints
3x+4y>=60
10x+5y>=100
Since the equations ask us to find the values to make the equations
greater than or equal instead of less than or equal, we need to
choose the smallest one in the Z row as the entering variable.
To choose which row, still use the one with the least value for
that variable. You still should add one slack variable to each
equation.
So the tableau looks like
-28 - 33
3 4 1 0 60
10 5 0 1 100
The one to add ( since we are trying to satisfy >= )
would be the column with the -28. The values of the variable
could be 20 for row 1 or 10 for row 2. Choosing the lesser,
we'll add row 2. We will also divide row 2 by 10 to get a 1
where the variable is.
0 -19 0 2.8 280
0 2.5 1 -0.3 30
1 0.5 0 0.1 10
Now the only column to add is the one with the -19 at the top.
Row 1: 30/2.5 = 12; Row 2: 10/0.5 = 20; select the first row.
Divide the first row by 2.5.
Multiply the first row by 38/5 and add to the first row.
Multiply the first row by -1/5 and add to the last row.
This should give you a simpleau matrix with nothing else to do.
The answers should be a total of $508, with 12 hours in the first
factory and only 4 hours in the second factory.
I've tried to review again and again, but this doesn't look right
to me right now. Send question again if it still needs to be done
and I'll try it again.
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Answers by Expert:
Scott A Wilson
Expertise
I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?
Experience
Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later.
I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman.
I tutored at Mathnasium for well over a year.
I worked at The Boeing Company for over 5 years.
I received an MS degreee in Mathematics from Oregon State Univeristy.
The classes I took were over 100 hours of upper division credits in mathematical courses such as
calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more.
I graduated with honors in both my BS and MS degrees.
Past/Present Clients: College Students at Oregon State University, various math people since college,
over 7,500 people on the PC from the US and rest the world.
Publications
My master's paper was published in the OSU journal.
The subject of it was Numerical Analysis used in shock waves and rarefaction fans.
It dealt with discontinuities that arose over time.
They were solved using the Leap Frog method.
That method was used and improvements of it were shown.
The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.
Education/Credentials
Master of Science at OSU with high honors in mathematics.
Bachelor of Science at OSU with high honors in mathematical sciences.
This degree involved mathematics, statistics, and computer science.
I also took sophmore level physics and chemistry while I was attending college.
On the side I took raquetball, but that's still not relevant.
Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State.
I was in near the top in most of my classes. In several classes in mathematics, I was first.
In a class of over 100 students, I was always one of the first ones to complete the test.
I graduated with well over 50 credits in upper division mathematics.
Past/Present Clients
My clients have been students at OSU, people nearby, friends with math questions,
and several people every day on the PC, and you're probably make one more.
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