It is desired to plan a 5day development program for the jun

It is desired to plan a 5-day development program for the junior sales managers of a major hardware chain. The program includes some combination of the following four activities: speakers, laboratory work, cases, and management games. It is estimated that for each day spent on an activity the weekly profits will increase as shown in Table I. The program lasts exactly 5 days, and it is assumed that no time is lost between shifts. In order to balance the program, the planner must make sure that no more than 3 days is spent on active or passive elements of the program. The active and passive percentages of each activity are shown in Table II. Also the company wishes to spend at least 03 day on each of the four activities. Finally, a total budget of $1500 is available, and the cost of each activity is shown in Table III. Formulate the appropriate LP to determine the 5-day plan by maximizing the weekly profit.

Solution

Variables:

Let

A= number of days for the activity speaker; A = A1 + A2 where A1= active & A2= passive element

B= number of days for the activity Laboratory work; B = B1 + B2 where B1= active & B2= passive

C= number of days for the activity Cases; C = C1 + C2 where C1= active & C2= passive element

D= number of days for the activity Management games; D = D1 + D2 where D1= active & D2= passive

Constraints:

A + B + C + D <= 5

A, B, C, D >= 0.5

A1 + B1 + C1 + D1 <= 3

A2 + B2 + C2 + D2 <= 3

       400A + 200B + 75C + 100D <= 1500

Objective:

The objective is to maximise total profit, i.e.

Maximise

(3200-400)(0.1A1 + 0.9A2) + (2000-200)(0.4B1 + 0.6B2) + (400-75)(1C1 + 0C2) + (2000-100)(0.6D1 + 0.4D2)