Logan, Ltd. makes two products, tables and chairs, which must be processed through assembly and finishing departments. Each table requires 4 hours to assemble and 3 hours to finish, but each chair requires 3 hours to assemble and 5 hours to finish. Assembly department has up to 60 hours available, and finishing department can handle up to 80 hours of work. The company wants to see at least 5 tables produced during the production. Due to the current on-hand inventory of chairs, the production of chairs must be less than the production of table. Each table yields a profit of $6, and each chair can be sold for a profit of $4. If you have your solutions in decimal, keep them as they are and do not round them to the nearest integer.
a. Show the feasible region graphically ((Draw a graph by using MS WORD's ‘Shapes' under the ‘Insert' tab).
b. What are the extreme points of the feasible region?
c. Find the optimal solution using the graphical method.
d. Are there any slack values? Are there any surplus values? (Hint: You can measure slack and surplus values at the optimal solution.)
e. Compute the shadow price of the assembly constraint.