8. An employment agency must provide the following laborers over the next 5 months:

Month No. of laborers 1

100 2

120 3

80 4

170 5

50 234 Chapter 5 Transportation Model and Its Variants Because the cost of labor depends on the length of employment, it may be more economical to keep more laborers than needed during some months of the 5-month planning horizon. The following table estimates the labor cost as a function of the length of employment:

Months of employment Cost per laborer ($)

1 100 2

130 3

180 4

220 5

250 Formulate the problem as a linear program. Then, using proper algebraic manipulations of the constraint equations, show that the model can be converted to a transshipment model, and find the optimum solution. (Hint: Use the transshipment characteristic in Problem 7 to convert the constraints of the scheduling problem into those of the transshipment model.)