Question: (a) A firm produces two goods A and B. The firm earns a profit of 300 from each unit of good A, and 200 from each unit of B. There are three stages of the production process. Good A requires 6 hours in production, then 4 hours in assembly, and finally 5 hours of packing. The corresponding numbers for B are 3, 6, and 5, respectively. The total number of hours available for the three stages are 54, 48, and 50, respectively. Formulate and solve the LP problem of maximizing profits subject to the given constraints. (b) Write down and solve the dual problem.
(c) By how much would the optimal profit increase if the firm gets 2 hours more preparation time and 1 hour more packing time?