Question

A small soft drinks company produces only two types of drink, Awefull (A) and Burpit (B). The production manager is concerned to get the best use of the bottling machinery at her disposal, and has asked you to investigate the problem. Essentially, the bottling process involves washing, filling and capping. One bottle of Awefull takes an average of 0.8 seconds to wash, 0.9 seconds to fill and 1 second to cap. A bottle of Burpit requires 1.2 seconds to wash, 1.5 seconds to fill and 1 second to cap. The company has one machine of each type (washing, filling and capping), and each machine is available for 10 hours each day. The company has long standing daily orders for at least 10000 bottles of Awefull, and at least 5000 bottles of Burpit, which must still be honoured. An investigation of the profit margins for the two drinks reveals that the contribution for Awefull is 20¢ per bottle, whilst Burpit generates 30¢ per bottle. The time to switch between productions of the two drinks is negligible, and the company is sure that they can sell all they produce.

Your file should contain the following information: LP model where decision variables are clearly identified, a graph showing all constraints with feasible region clearly identified and a table showing all extreme corners in the feasible region with optimal solution.

Formulate a linear programming model for this problem and solve it using the graphical method. (Important)

Answer 1

Number of bottles of Awefull=X1

Number of bottles of Burpit=X2

Objective function Maximize Revenue Generation=20*X1+30*X2

Constraints:

Washing: 0.8*X1+1.2*X2=<36000(10*60*60)

Filling: 0.9*X1+1.5*X2=<36000

Cap: 1*X1+1*X2=<36000

X1>=10000

X2>=5000

using Graphical method, I have prepared the Graph as shown below:

hence,

Number of bottles of Awefull=30000

Number of bottles of Burpit=6000

Objective function Maximize Revenue Generation=780000