Formulate the linear program associated with the following problem. Wool Style I
ID: 3009434 • Letter: F
Question
Formulate the linear program associated with the following problem. Wool Style Inc. produces high-quality slacks and dresses for women.
Each pair of slacks requires 1.8 hours of cutting time and 0.55 hours of sewing time, uses 7 yards of material, and provides a profit contribution of $175. Each dress requires 0.85 hours of cutting time and 0.6 hours of sewing time, uses 5 yards of material, and provides a profit contribution of $150. For the coming week, 200 hours of cutting time, 180 hours of sewing time, and 1200 yards of fabric are available. Additional cutting and sewing time can be obtained by scheduling overtime for these operations. Each hour of overtime for the cutting operation increases the hourly cost by $15 and each hour of overtime for the sewing operation increases the hourly cost by $10. A maximum of 100 hours of overtime can be scheduled. Marketing requirements specify a minimum production of 100 slacks and 75 dresses.
Let S = the number of slacks manufactured,
D = the number of dresses manufactured,
OT1 = the number of sewing overtime hours, and
OT2 = the number of cutting overtime hours.
Formulate the linear program for this problem. Explicitly state the objective function, model constraints (and their meaning), and the non-negativity statement using the decision variables defined above.
Explanation / Answer
The objective is to maximize the profit , so we'll have to subtract the over time expense from the profit
so the objective function is maximize Z = 175*S + 150*D - 10*OT1 - 15*OT2
the constraints are :
cutting time for 1 pair slack is = 1.8 hour
and that for 1 dress = .85 hours
=> 1.8S + .85D <= 200
sewing time for 1 pair of slack is = .55 hours
sewing time for 1 dress is = .6 hours
=> .55S + .6D <= 180
1 pair of slack uses = 7 yards of material
1 dress uses = 5 yards of material
=> 7S + 5D <= 1200
the over time is not supposed to exceed 100 hours
=> OT1 + OT2 <= 100
Marketing requirements specify a minimum production of 100 slacks and 75 dresses
=> S >= 100
D >= 75