Convert the constraints into linear equations by using slack variables. Maximize
ID: 3141183 • Letter: C
Question
Convert the constraints into linear equations by using slack variables. Maximize z = 2x_1 + 8x_2 Subject to: X_1 + 8x_2 lessthanorequalto 15 8x_1 + 9x_2 lessthanorequalto 25 x_1 greaterthanorequalto 0 x_2 greaterthanorequalto 0 A) x_1 + 8x_2 = s_1 + 15 8x_1 + 9x_2 = s_2 + 25 B) x_1 + 8x_2 + s_1 lessthanorequalto 15 8x_1 + 9x_2 + s_2 lessthanorequalto 25 C) x_1 + 8x_2 + s_1 greaterthanorequalto 15 8x_1 + 9x_2 + s_2 greaterthanorequalto 25 D) x_1 + 8x_2 + s_1 = 15 8x_1 + 9x_2 + s_2 =25 Introduce slack variables as necessary and write the initial simplex tableau for the problem. Maximize z = 4x_1 + x_2 subject to: 2x_1 + 5x_2 lessthanorequalto 15 3x_1 + 3x_2 lessthanorequalto 3 x_1 greaterthanorequalto 0, x_2 greaterthanorequalto 0Explanation / Answer
17.
Slack variables are positive valued variables added to the left hand side of a less than or equal to constraints in a LPP in order to make it an equality. They are generally represented by s1,s2 etc.
In the given problem, the first constraint is x1 + 8x2 <= 15.
By adding the slack variable s1 the constraint can be written as x1 + 8x2 + s1 = 15
The second constraint in the given problem is 8x1 + 9x2 <= 25.
By adding the slack variable s2 the constraint can be written as 8x1 + 9x2 + s2 = 25.
Hence the answer is D.
D) x1 + 8x2 + s1 = 15
8x1 + 9x2 + s2 = 25
18)
The problem can be written in the standard form as follows.
Maximize Z = 4x1 + x2 + 0 s1 + 0s2
subject to the constraints,
2x1 + 5x2 + 1s1 +0s2 = 15
3x1 + 3x2 + 0s1 + 1s2 = 3,
where s1 and s2 are the slack variables and x1, x2, s1,s2 >= 0
Now the initial simplex table is as follows.
Hence the answer is A.
In the above table, first row represents variable names , second row represents the coefficients of variables in the first constraint, third row represents the coefficients of variables in the second constraint and the last row represents the coefficients of variables in the objective function.
x1 x2 s1 s2 z solution 2 5 1 0 0 15 3 3 0 1 0 3 4 1 0 1 0 0Related Questions
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