Question

You are in charge of project scheduling for InfluFree Inc, a leading manufacturer of flu (influenza) vaccine. Producing flu vaccine involves the steps shown in the Table l below. Purification and testing stage I (activity D) can be accelerated by using catalyst Alpha. Each gallon of Alpha used for activity D will shorten its duration by one day. Similarly, purification and testing stage II. (Activity E) can be accelerated by using catalyst Beta. Each gallon of Beta used for activity E will shorten the duration of E by one day. Once used to shorten an activity, catalyst cannot be recovered for subsequent use. InfluFree has available 60 gallons of catalyst Alpha, and 65 gallons of catalyst Beta. The entire quantity of Alpha and Beta is available at the beginning of the project. Technical limitations mean that overall at most 110 gallons of catalysts may be used to shorten activities. Provide an LP model and solve the problem using Excel LP solver. Explain if any other optimal solution is possible, that is, specify if it is feasible to have the starting dates of selected activities changed without affecting the production cost.

Answer 1

The student asked for an LP model to optimize the scheduling for flu vaccine production involving the use of catalysts and provided constraints, including limited catalyst supply and technical limitations. Excel Solver is required to find the optimal solution, and alternative optimal solutions could be explored regarding the starting dates of selected activities.

Step-by-step explanation:

The student's question involved creating an LP (Linear Programming) model for a flu vaccine production scheduling problem at InfluFree Inc., where catalysts are used to accelerate certain stages of vaccine purification and testing. The goal is to determine how to allocate the catalysts Alpha and Beta to minimize the duration of the production, given that there is a limited supply of these catalysts and that no more than 110 gallons of them can be applied to the process in total. To provide an accurate answer, the LP model would need to assign decision variables to the quantities of Alpha and Beta used in each stage, set constraints based on the availability and technical limitations of catalysts, and include an objective function to minimize the total production time. Excel Solver can be used to find the optimal solution within these parameters. Moreover, if alternative optimal solutions with different starting dates exist without affecting production cost, these could be presented as well.