Linear Programming Applied 1Make up and describe a business

Linear Programming Applied

1.Make up and describe a business situation that could be solved using linear programming. (5 points)

2. Identify and describe the two variables you are solving for. (5 points)

3. Write out all the inequalities defining the restrictions on those variables. (5 points)

4. Describe and construct the equation defining the objective function (what you are trying to maximize or minimize). Example: profit, revenues, cost, etc. (3 points)

Solution

High Quality furniture Ltd. Manufactures two products, tables & chairs. Both the products have to be processed through two machines Ml & M2 the total machine-hours available are: 200 hours ofM1 and 400 hours of M2 respectively. Time in hours required for producing a chair and a table on both the machines is as follows:

Time in hours:

Profit from the Sale of table is Rs. 40 and that from a chair is Rs. 30 determine optimal mix of tables & chairs so as to maximized the total profit

Let x1 = no. of tables produced and X2 = no. of Chairs produced

The objective function for maximizing the profit is given by maximize Z=50x1 +30x2 ( objective function ) ( Since profit per unit from a table and a chair is Rs. 50 & Rs. 30 respectively).

List down all the constraints. (i) Total time on machine M1 can not exceed 200 hours. 7x1+ 4x2 200 ( Since it takes 7 hours to produce a table & 4 hours to produce a chair on machine M1) (ii) Total time on machine M2 cannot exceed 400 hours.

7x1+ 4x2 200 ( Since it takes 5 hours to produce both a table & a chair on machine M2)

Presenting the problem. The given problem can now be formulated as a linear programming model as follows: Maximise Z = 50x1 + 30x2 Subject: : 7x 4x 200 1 + 2 5x 5x 400 1 + 2 Further; x1 x 0 + 2 (Since if x1 & x2 < 0 it means that negative quantities of products are being manufactured – which has no meaning).