GG Manufacturing is the distributor for medical grade freezer. Their two signature products are: Ultra Freeze and Nano Freeze, whose profits are $9000 and $12000, respectively. The company showroom has a maximum storage capacity of 50 cubic feet and each freezer takes up 5 cubic feet of storage. To secure the freezer, a special locking mechanism has to be attached to the freezer. Ultra Freeze requires 15 of such locking mechanism, while Nano Freeze requires 8 such locking mechanisms. In total, there are 120 locking mechanism available in the showroom. Every freezer in the showroom needs to be protected with protection panel, where each unit of Ultra Freeze needs 1 while Nano Freeze needs 2 of such panel. There are only 16 protection panels available in the showroom. The sales team also cautioned that due to the uncertain economic situation, the daily demand for each type of freezer is expected to cap at 7 units each.
(a) Based on the above scenario, develop the case as a linear programming model to determine the ideal units of freezer to be stocked up daily.
(b) Apply graphical and simultaneous equation approach to solve the linear programming model. You are required to identify the feasible region, solve for each corner point and identify the optimal solution.
(c) Solve for the sensitivity output using Microsoft Excel Solver.
(d) Interpret the reports and discuss the following scenarios (without re-solving it using Microsoft Excel Solver):
(i) If the profit on Nano Freeze is reduced to $6000, explain if there will be any changes to the original optimal mix and total profit?
(ii) The maximum storage capacity turns out to be actually 45 cubic feet instead of 50 cubic feet. How will this affect the solution?