# Question

Consider the following problem.

Maximize Z = c1x1 + c2x2 + c3x3,

Subject to

and

x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.

Note that values have not been assigned to the coefficients in the objective function (c1, c2, c3), and that the only specification for the right-hand side of the functional constraints is that the second one (2b) be twice as large as the first (b).

Now suppose that your boss has inserted her best estimate of the values of c1, c2, c3, and b without informing you and then has run the simplex method. You are given the resulting final simplex tableau below (where x4 and x5 are the slack variables for the respective functional constraints), but you are unable to read the value of Z*.

(a) Use the fundamental insight presented in Sec. 5.3 to identify the value of (c1, c2, c3) that was used.

(b) Use the fundamental insight presented in Sec. 5.3 to identify the value of b that was used.

(c) Calculate the value of Z* in two ways, where one way uses your results from part (a) and the other way uses your result from part (b). Show your two methods for finding Z*.

Maximize Z = c1x1 + c2x2 + c3x3,

Subject to

and

x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.

Note that values have not been assigned to the coefficients in the objective function (c1, c2, c3), and that the only specification for the right-hand side of the functional constraints is that the second one (2b) be twice as large as the first (b).

Now suppose that your boss has inserted her best estimate of the values of c1, c2, c3, and b without informing you and then has run the simplex method. You are given the resulting final simplex tableau below (where x4 and x5 are the slack variables for the respective functional constraints), but you are unable to read the value of Z*.

(a) Use the fundamental insight presented in Sec. 5.3 to identify the value of (c1, c2, c3) that was used.

(b) Use the fundamental insight presented in Sec. 5.3 to identify the value of b that was used.

(c) Calculate the value of Z* in two ways, where one way uses your results from part (a) and the other way uses your result from part (b). Show your two methods for finding Z*.

## Answer to relevant Questions

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