Use integer variables for the following problems.

Problem 1

The NW Shopping Mall conducts special events to attract potential patrons. Among the events that seem to attract teenagers, the young/middle-aged group, and senior citizens, the two most popular are band concerts and art shows. Their costs per presentation are $1,500 and $3,000, respectively. The total (strict) annual budget allocated to the two events is $15,000. The mall manager estimates the attendance as follows:

The manager has set minimum goals of 1000, 1200, and 800 for the attendance of teenagers, young/middle-aged group, and seniors, respectively. Formulate and solve the problem as a goal programming model with integer variables assuming that all goals have equal weight. It is OK to overachieve on the attendance goals, but the manager will not accept a solution that exceeds the $15,000 budget.

Problem 2

In Problem 1, suppose that the goal of attracting seniors is twice as important as either of the other two goals (attracting teenagers and young/middle-aged people). Find the associated solution, and check if all the goals have been met.

Problem 3

In Problem 1, suppose that the goals set for teenagers, young/middle-aged group, and seniors are referred to as G ₁ , G ₂ , and G ₃ , respectively. Solve the problem for each of the following priority orders ( G _i > G _j means goal G _i has higher priority than goal G _j ).

1. G ₁ > G ₂ > G ₃
2. G ₃ > G ₂ > G ₁

In each case, find the associated solution and check if all the goals have been met.

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