Let,
xi = yards of fabric i to produce on Jaquard loom
yi = yards of fabric i to produce on Northop loom
pi = yards of fabric i to be purchased from external supplier
Objective is to minimize cost = Min 0.53x1 + 0.6x2 + 0.71x3 + 0.6y2 + 0.71y3 + 0.81p1 + 0.85p2 + 0.84p3
Subject to following constraints,
1. Demand Constraints
x1+p1 = 50000 (Demand should be exactly matched)
x2+y2+p2 = 62000 (Demand should be exactly matched)
x3+y3+p3 = 35000 (Demand should be exactly matched)
2. Capacity constraints
available hours for Jaquard = 24 hours/day * 7 days/week* 12
weeks*2 looms = 4032
capacity of Jaquard for fabric 1 = 5.6 yards/hour we can say per hour capacity = 1/5.6 per hour
1/5.6 x1 + 1/5.2 x2 + 1/4.8 x3 <= 4032
or,0.17857x1 + 0.19230X2 + 0.20833X3 <= 4032 -----(1)
available hours for Northorp = 24 hours/day * 7 days/week* 12
weeks*10 looms = 20160
1/4.8Y2 + 1/4.5Y3 <= 20160
OR, 0.20833Y2 + 0.22222Y3 <= 20160
xi,yi,pi >= 0 (non-negativity constraints)
Solving in excel solver we get,
x1 = total amount of fabric 1 to be produced on Jaquard = 22579.38
Correct answer is 22579.2 (Ans)
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