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Question 1150952: A firm has produced three products A, B, and C. Each of which passes through three departments: Fabrication, finishing, and packaging. Each unit of product A requires 3,4, & 2 hours; a unit of B requires 5,4, and 4 hours while each unit of product C requires 2,4 and 5 hours respectively in three departments. Every day, 60 hours are available in the fabrication departments, 72 hours in the finishing department and 100 hours in the packaging department. If the unit contribution of product A is usd$ 5, of product B is 10 and of product C is usd$ 8, determine the number of units of each of the products, that should be made each day to maximize the total contribution.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! results are shown below:
make a chart as shown below:
product A B C
number of units x y z
fabricate hours 3 5 2 <= 60
finish hours 4 4 4 <= 72
packaging hours 2 4 5 <= 100
objective function 5 10 8 maximize
x represents the number of units of product A.
y represents the number of units of product B.
z represents the number of unitis of product C.
x, y, z >= 0 is assumed by the simplex method tool used.
that tool can be found at https://www.zweigmedia.com/RealWorld/simplex.html
the tool provides a method to find the optimal solution through the use of the simplex method of analysis.
that is fairly complex and tedious to do manually.
the tool mechanizes the process and provided a solution immediately if the inputs are modeled correctly.
here's a tutorial on the simplex method from the same people who supplied the tool.
doing it manually is not an easy task, but it can be done, if necessary.
https://www.zweigmedia.com/RealWorld/tutorialsf4/frames4_3.html
there are lots of references on the web, including video tutorials that may be helpful.
just do a search on "simplex method of solving linear programming problems" or some such search string.
according to the tool, your optimal solution is:
maximum profit = 160 when producing and selling 0 units of product A and 8 units of product B and 10 units of product C.
0 units of product A, 8
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