Toolco has contracted with AutoMate to supply their automotive discount stores with wrenches and chisels. AutoMate’s weekly demand consists of at least 1570 wrenches and 1250 chisels. Toolco cannot produce all the requested units with its present one-shift capacity, and must use overtime and possibly subcontract with other tool shops. The result is an increase in the production cost per unit, as shown in the following table. Market demand restricts the ratio of chisels to wrenches to at least 2:1.

Tool Production type Weekly production range (units) Unit cost ($)

Wrenches Regular 0–500 2.00 Overtime 501–800 2.80 Subcontracting 8019∞ 3.00 Chisel Regular 0–620 2.10 Overtime 621–900 3.20 Subcontracting 9019∞ 4.20

(a) Formulate the problem as a linear program, and determine the optimum production schedule for each tool.

(b) Explain why the validity of the model is dependent on the fact that the unit production cost is an increasing function of the production quantity.

(c) Solve the model using AMPL, Solver, or TORA.