Question 1 (10 Marks)

The production manager for a soft drink company is considering the production of two kinds of soft drinks: regular (R) and diet (D). Two of her limited resources are production time (100 minutes per day) and syrup (1 of the ingredients), limited to 80 gallons per day. To produce a carton of regular soft drink requires 2 minutes and 1 gallon of syrup, while a carton of diet soft drink needs 1 minute and 1 gallon of syrup. Profits for a carton regular soft drink are RM50.00 and profits for a carton diet soft drink are RM18.00.

i. Develop a linear programming model for the above problem (2 marks)

ii. Show the complete steps to get the optimal solution using graphical solution and explain the answer. (6 marks)

iii. What are the value of slack variables associated with the production time and syrup constraint? Explain the answer. (2 marks)