The PQ Piston Plant makes two sizes of pistons for reciprocating engines. Their plant has four machines. Currently, the demand for their products is 100 'p" pistons per week:, and 50 "Q" pistons per week.
The financial information for these products is as follows:
Product P: Selling Price $180 Materials $90
Product Q: Selling Price $200 Materials $80
Fixed Operating Expenses (including all labor) is $12,000 per week a
Three of the machines have enough capacity to produce all units demanded by the market. The fourth machine, Machine B, cannot produce all the demanded units. The B machine must run 15 minutes for each Product P it processes, and 30 minutes for each Product Q it produces. The plant operates 40 hours (2400 minutes) per week.
Please determine the product mix for this plant that produces the greatest net profit per week. Remember: the critical measurement is throughput (selling price minus materials) per minute of B operation. How many P and how many Q pistons will result in the greatest profit for this plant. Please show your calculations in both dollars and quantities.