a) Formulate a linear programming model that can be used to determine how many units of each component to manufacture and how many units of each component to purchase. Assume that component demands that must be satisfied are 6000 units for component 1, 4000 units for component 2, and 3500 units for component 3. The objective is to minimize the total manufacturing and purchasing costs.
b) What is the optimal solution? How many units of each component should be manufactured and how many units should be purchased?
c) Which departments are limiting Benson’s manufacturing quantities? Use the dual price to determine the value of an extra hour in each of these departments.
d) Suppose that Benson had to obtain one additional unit of component 2. Discuss what the dual price for the component 2 constraint tells us about the cost to obtain the additional unit.