Chapter 3.9, Problem 11P
Formulation of LP:
Let,
xi be the pounds of product sold, for (i=1,2,3).
R1 be the pounds of raw material bought and turned into A and R2 be the pounds of law material bought and turned into B.
Let, Pi be the pounds of product i processed further, for (i=1,2,3).
The objective is to maximize chemo’s profit.
The profit=(cost of product 1 per pound)(ponds of product 1 sold)+(cost of product 2 per pound)(ponds of product 2 sold) +(cost of product 3 per pound)(ponds of product 3 sold)-(cost of raw material per lb)(pounds of row material bought and turned into A)
-(cost of raw material per lb)(pounds of row material bought and turned into B)-(cost per lb)(pounds of product A processed further) -(cost per lb)(pounds of product B processed further)
=10x1+12x2+20x3-5R1-5R2-3P1-2P2
Thus the objective function is,
Maximize, Z=10x1+12x2+20x3-5R1-5R2-3P1-2P2
Constraint 1:
At most, 1lb of product A can be produced from the raw material purchased.
(Pounds of raw material bought and turned into A-Pounds of pounds of product A proceeded) ≤Pounds of product A
R1-P1≤x1R1-P1-x1=0
Constraint 2:
At most, 1lb of product A can be produced from the raw material purchased and 0