Weenies and Buns is a food processing plant which manufacturer’s hot dogs and hot dog buns. They grind their own flour for the hot dog buns at a maximum rate of 200 pounds per week. Each hot dog bun requires 0.1 pound of flour. They currently have a contract with Pig land, Inc. which specifies that a delivery of 800 pounds of pork product is delivered every Monday. Each hot dog requires ¼ pound of pork product. All the other ingredients in the hot dogs and hot dog buns are in plentiful supply. Finally the labour force at Weenies and Buns consists of 5 employees working full time (40 hours per week each). Each hot dog requires 3 minutes of labour, and each hot dog bun requires 2 minutes of labour. Each hot dog yields a profit of $0.20, and each bun yields a profit of $0.10.

a) Use the graphical solution to determine the number of hot dogs and hot dog buns to produce each week that would maximize profit.

b) Determine the optimality range of the ratio of hot dog to hot dog buns that will keep the solution unchanged.

c) Determine the worth per unit change in the availability of the pork product and its range of applicability.