Solve the following problem by the simplex method. After leaving the Lotsakia Co

Question

Solve the following problem by the simplex method. After leaving the Lotsakia Corporation (sec test 1). You are hired by Petswirld, manufacturer of stuff for pets. They make three types of cat toys; type A, type 2, and type III. A toy of each type sells for dollar 12, dollar 15, and dollar 5, respectively. Each type A toy requires 2 minutes of painting and I minute of assembly. Each type 2 toy requires 2 minutes of painting and 4 minutes of assembly. Each type III toy requires 1 minute of painting and 3 minutes of assembly. Every day the painting machine is available for cat toys for 24 minutes, and the assembly machine is available for 36 minutes. How many of each type of toy should be produced to maximize the revenue? What is the maximum revenue?

Explanation / Answer

x: type A

y: type 2

z:type III

using excel to solve the problem

Tableau #1
x y z s1 s2 p   
2 2 1 1 0 0 24   
1 4 3 0 1 0 36   
-12 -15 -5 0 0 1 0

Tableau #2
x y z s1 s2 p   
1.5 0 -0.5 1 -0.5 0 6
0.25 1 0.75 0 0.25 0 9
-8.25 0 6.25 0 3.75 1 135

Tableau #3
x y z s1 s2 p   

1 0 -0.333333 0.666667 -0.333333 0 4   
0 1 0.833333 -0.166667 0.333333 0 8   
0 0 3.5 5.5 1 1 168   

Optimal Solution: p = 168; x = 4, y = 8, z = 0

maxZ=12x+15y+5z subject to 2x+2y+1z<=24 x+4y+3z<=36

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