Posh Fragrance is a company that supplies tea leaves to the regional hotels and restaurants. Their two best seller tea leaf blends are Flora1 and Scent2. Due to the upcoming festive season, there is a consolidated order commitment for at least 150 kg of Flora1, and 200 kg of Scent2. To produce 1 kg of Flora1, it should contain at most 55 percent dried figs while each kg of Scent2 should contain at least 65 percent of orange peel. The source for orange peel comes from two mixtures; mixture Alpha and mixture Beta. Mixture Alpha contains 70 percent orange peel and 20 percent dried figs, while mixture Beta contains 25 percent orange peel and 60 percent dried figs. Mixture Alpha costs 85 cents per kg and mixture Beta costs 40 cents per kg. The company CEO would like to know the cost-effective way of mixing Alpha and Beta.
(a) Develop the portfolio selection case as a linear programming problem. Please explain clearly how you choose the decision variables, formulate the objective function and constraints.
(b) Solve for the optimal solution using Microsoft Excel Solver. Show the relevant solution output and sensitivity output.
(c) Interpret the reports and discuss the following scenarios (without resolving it using Microsoft Excel Solver):
(i) If the cost of Mixture Alpha is 50 cents, explain if there will be any changes to the original optimal mix?
(ii) If the order for Flora1 is actually 50kg instead of 150kg, what would be the implications on the total cost on acquiring mixture Alpha and Beta?