As a result of a recent decision to stop production of toy guns that look too real, the Super Slayer Toy Company is planning to focus its production on two futuristic models: beta zappers and freeze phasers. Beta zappers produce $2.50 in profit for the company, and freeze phasers, $1.60.

The company is contracted to sell 10 thousand beta zappers and 15 thousand freeze phasers in the next month, but all that are produced can be sold. Production of either model involves three crucial steps: extrusion, trimming, and assembly.

Beta zappers use 5 hours of extrusion time per thousand units, 1 hour of trimming time, and 12 hours of assembly. Corresponding values per thousand units of freeze phasers are 9, 2, and 15.

There are 320 hours of extrusion time, 300 hours of trimming time, and 480 hours of assembly time available over the next month. (An optimization output appears in Table 6.6.)

(a) Briefly explain how this problem can be modeled by the linear program:

max 2500x1 + 1600x2 s.t. x1 Ú 10 x2 Ú 15 5x1 + 9x2 … 320 1x1 + 2x2 … 300 12x1 + 15x2 … 480 x1, x2 Ú 0

(b) Identify the resource associated with the objective function and each main constraint in part (a).

(c) Identify the activity associated with each decision variable in part (a).

(d) Interpret the left-hand-side coefficients of each decision variable in part

(a) as inputs and outputs of resources per unit activity.