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1. Formulate a preemptive goal programming model for this situation.

Decision variables:

= amount that the company can bill on Partner for Job 1

= amount that the company can bill on Partner for Job 2

= amount that the company can bill on Partner for Job 3

= amount that the company can bill on Senior employee for Job 1 = amount that the company can bill on Senior employee for Job 2

= amount that the company can bill on Senior employee for Job 3

= amount that the company can bill on Junior employee for Job 2

= amount that the company can bill on Junior employee for Job 3

= the number of Partner should be hired

= the number of Senior employee should be hired

= the number of Junior employee should be hired

Goal constraints:

Goal 1: Monthly billing should exceed RM68,000

will minimize the underachievement variable

Goal 2: At most 1 partner should be hired

will minimize the overachievement variable

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Goal 3: At most 3 senior employees should be hired

will minimize the overachievement variable

Goal 4: At most 5 junior employees should be hired

will minimize the overachievement variable

Hard constraints:

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Therefore,

Minimize

Subject to:

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3. Solve Question 2 by using any LP package. (Example: LINDO, Spreadsheet)

We will rewrite the problem using , , , , , , and variables because it is easier

to type the problem in LINGO with that notation without getting confused with the + and signs.

Therefore the new problem is:

Min

subject to

To solve with LINGO, we must minimize one variable at a time in the objective function. So, we

will first minimize .

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We will write in LINGO the following problem:

Min

subject to

and press Solve.

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If Goal 1 is achieved, then . We will get the following printout:

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We will note the objective function is 0, and the values of

and .

To solve for the second goal, we add , to the constraints as follows and this time we are

minimizing

, the second variable in the objective function.

By putting , we are ensured that the first goal is met. By solving we will get a printout as

follows:

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If Goal 2 is achieved, then .

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We will note the objective function is 0, and the values of

and .

To solve for the third goal, we add , to the constraints as follows and this time we are

minimizing

, the third variable in the objective function.

By putting , we are ensured that the second goal is met. By solving we will get a printout

as follows:

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If Goal 3 is achieved, then .

We will note the objective function is 0, and the values of

and .

To solve for the fourth goal, we add , to the constraints as follows and this time we are

minimizing , the fourth variable in the objective function.

By putting , we are ensured that the third goal is met. By solving we will get a printout as

follows:

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If Goal 4 is achieved, then .

We will note the objective function is 0, and the values of

and .

The optimal solution is:

Therefore,

The number of employees should be hired by Halim&Lee

= 1 partner + 3 senior employees + 5 junior employees

= 9 employees