SOLUTION: A company is planning to buy new fork hoists for material handling, there are two models that will serve their needs, Model M & model R. The warehouse supervisor feels that a minim

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Question 1154669: A company is planning to buy new fork hoists for material handling, there are two models that will serve their needs, Model M & model R. The warehouse supervisor feels that a minimum of 3 model M hoists and 5 model R hoist will be needed. The supplier has 8 model M hoist and 10 model R hoist on hand for delivery. The company purchasing agent has decided that no more than 14 hoists can be purchased. Model M can handle 12,000 kilograms per hour and model R can handle 10,000 kilograms per hour. What number of hoist of each model should be purchased for maximum weight handling capacity? What is the maximum weight handling capacity?

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
here's your answer two ways.
first uses a simplex method tool.
second uses graphical method.
both give you the same answer.
max capacity is 156000 kilograms using 8 type M and 6 type R.
simplex method tool can be found at
https://www.zweigmedia.com/RealWorld/simplex.html
graphing calculator can be found at:
https://www.desmos.com/calculator
your objective function is c = 12000x + 10000y
c stands for capacity.
x represents type M
y represents type R
your constraint functions are:
x >= 3
y >= 5
x <= 8
y <= 10
x + y <= 14
using the desmos.com/calculator you graph the opposite of the inequalities.
you can see the functions used there.
you then find the unshaded portion of the graph and you look at the corner points to find the maximum capacity by evaluating each corner point using the objective function.
for example:
at the point (8,6), you get 12000 * * + 10000 * 6 = 156000
here's the results from using both methods.