Serious Toys Unlimited produces three types of building block sets for kids — Advanced Sets (A), Beginner Sets (B) and Intermediate Sets (C). The company has a total of 600 minutes available for production (280 minutes worth of labor time and 320 minutes worth of machine time). An advanced set requires 2 minutes of machine time and 9 minutes of labor time. A beginner set requires 8 minutes of machine time and 4 minutes of labor time. An intermediate set requires 4 minutes of machine time and 5 minutes of labor time. The material used to manufacture these sets is plastic, where 6 pounds is needed for each advanced set, 3 pounds is needed for each intermediate set and 5 pounds is needed for each beginner set. While an advanced set only earns a profit of $1.2, an intermediate set earns a profit of $1.4 and each beginner set earns $1.6 of profit. To fulfill its contract obligations, Serious Toys needs to produce at least 18 beginner sets. The company wants to determine the number of advanced, beginner and intermediate sets it can produce in order to meet its obligations and maximize profit, given that they only have 300 pounds of plastic to use.
1. construct the correct objective function for the above LP problem
2. construct the correct plastic constraint for the above LP problem
3. construct the correct machine constraint for the above LP problem
4. How many constraints are there in the Serious Toys Unlimited LP problem?