1. Consider a plant consisting of three machines that make two products, P and Q. Product P costs $50 in raw materials and requires 2 hours on machine 1 and 2 hours on machine 3. Product Q costs $100 in raw materials and requires 2.5 hours on machine 2 and 1.5 hours on machine 3. Thus, both products require a total of 4 hours of machine and 4 hours of labor time. Labor cost rate is $20 per hour (including benefits etc.), but,for simplicity, assume that total labor costs are fixed and included in non-material costs. The plant runs an average of 21 days per month with two shifts or 16 working hours per day, for a total of 336 hours per month. Nonmaterial expenditures to run the plant (labor, supervision, administration, etc.) are $100,000 per month. Both products sell of $600 per unit and make use of exactly the same amount of overhead. Marketing estimates a demand of no more than 140 units per month for each product. Also, to maintain market position, the company needs to produce at least 75 units of P per month.

Product Name	Price ($/unit)	Raw Material Cost ($/unit)	Total Labor Hours/unit	Unit Cost	Min; Max Monthly Demand
P	600	50	4	130	75; 140
Q	600	100	4	180	0; 140

If we prioritize P and Q using the bottleneck ratio method, determine the production plan and the resulting profit? Show intermediate bottleneck ratio and other calculations (in sufficient explanatory detail). Briefly explain how you would determine if the solution from the bottleneck ratio method maximizes profit or not.