State the following problem in a form for which the simplex matrix can be formed (that is, as a maximization problem with constraints).
A)
B)
C)
D)

Question

State the following problem in a form for which the simplex matrix can be formed (that is, as a maximization problem with  constraints). ​  ​
A)​ ​ 
B)​ ​ 
C)​ ​ 
D)​ ​

Quizplus · Accepted Answer

To formulate a linear programming problem, we need to have an objective function to maximize or minimize, and a set of constraints. In this case, we have an objective function given by 11eb0d3b_980c_5b05_9790_7d2e0cdea79e_TB1243_00, which we want to maximize. The constraints are given by 11eb0d3b_980c_5b06_9790_6fa7ac61bfe8_TB1243_00 to 11eb0d3b_980c_5b09_9790_79b75c1379f9_TB1243_00, which are all linear inequalities. We can rewrite these inequalities as equations by adding slack variables and then use matrix operations to solve the system.

Since we have 11 variables and 4 constraints, we can rewrite the problem in the following form:

Maximize:
Z = 11eb0d3b_980c_5b05_9790_7d2e0cdea79e_TB1243_00

Subject to: 
11eb0d3b_980c_5b06_9790_6fa7ac61bfe8_TB1243_00 
11eb0d3b_980c_5b07_9790_15492a7238cd_TB1243_00 
11eb0d3b_980c_5b08_9790_4b13f7650492_TB1243_00 
11eb0d3b_980c_5b09_9790_79b75c1379f9_TB1243_00

This can be rewritten as a standard form problem with slack variables:

Maximize:
Z = 11eb0d3b_980c_5b05_9790_7d2e0cdea79e_TB1243_00

Subject to: 
11eb0d3b_980c_5b06_9790_6fa7ac61bfe8_TB1243_00 + x1 = 0 
11eb0d3b_980c_5b07_9790_15492a7238cd_TB1243_00 + x2 = 0 
11eb0d3b_980c_5b08_9790_4b13f7650492_TB1243_00 + x3 = 0 
11eb0d3b_980c_5b09_9790_79b75c1379f9_TB1243_00 + x4 = 0

where x1, x2, x3, and x4 are slack variables.

Now we can form the simplex matrix and apply the simplex algorithm to find the optimal solution. However, without additional information about the coefficients and constraints, we cannot determine the optimal solution or feasibility of the problem.

State the Following Problem in a Form for Which the Simplex