Linear Programming and Aggregate Planning Problems 1. Product-Mix. Referring to the Perfect Plant i.e., PQ Example from your lecture notes and the LP formulation we developed in the class, solve the above linear program using graphical approach described in the CD-ROM Chapter 5, find out what is the optimal product mix and what is the total throughput this plant can realize. Note: If you know how to use EXCEL and its SOLVER, you don't have to use graphical approach to find optimal solution to this problem. Instead find the optimal solution to the next LP problem using the Solver. Go to Blackboard Quantitative Assignment section to see an example Excel Template for the PQ Example. 2. Product-Mix. Referring to the ADF Company or the TOC Simulator (see your Home Work Assignment #2), formulate a Linear Program for TOC Simulator Example by identifying (i) the decision variables, (ii) objective function, and (iii) constraint functions. Can this problem be solved using graphical approach? Discuss. (Note: If you solved problem #1 using graphical method, then you don't have to find the optimal solution to this problem) 3. Aggregate Planning: The Hefty Beer Company is constructing an aggregate plan for the next 12 months. Although several types of beers are brewed at the Hefty plant and several container sizes are bottled, the management has decided to use gallons of beers as the aggregate measure of capacity. The demand for beer over the next 12 months is forecast as: Demand ('000 gallons) Jan Feb 250 250 300 Mar Apr. May 350 400 June 450 600 July Aug. 550 Sept. Oct. Nov. Dec. 430 420 400 400 Background Information: Beginning Inventory: 50,000 gallons Production/worker/month 10,000 gallons Initial number of workers 40 workers Hiring costs $1000 per worker Layoff costs Unit cost Overtime unit cost $2,000 per worker $2 per gallon $2.15 per gallon Carrying cost/unit/month 3% of the unit cost Desired ending inventory 50,000 gallons The management of the Hefty Brewery would like to consider three aggregate plans: a. Level workforce (Pure Level Strategy) b. Vary the workforce (Pure Chase Strategy) C. Chase strategy plus overtime i.e., use overtime when demand exceeds the maximum capacity of 450,000 gallons. Discuss which aggregate plan should the management team select? Discuss the implications of the chosen plan from Generic Business Strategies viewpoint as well as from TOC Mindset viewpoint.