Hat produc. Gentlemen Ladies
Capacity in mins. Cutting 5 10 480
Knitting 9 8 480
Vol produc. x1 x2
Profitability 50 75
The primary LP is as follows max50x1+75x2
5x1+10x2≤480
9x1+8x2≤480
x1,x2≥0
Based on some standard procedures, we formulate the dual problem as follows min480y1+480y2
5y1+9y2≥50
10y1+8y2≥75
y1,y2≥0
The y variables in the dual problem represent the shadow prices or dual prices associated with the constraints of the primal problem. Specifically, y1 represents the shadow price for the constraint on the capacity of cutting operations, indicating the change in profitability for each additional unit of capacity allowed in cutting. Similarly, y2 represents the shadow price for the constraint on the capacity of knitting operations. These shadow prices help understand the marginal impact on profitability for relaxing or tightening the constraints in the primal problem.