Answer to Question #220898 in Operations Research for shazia

Question

Exercise Sheet

Q1. A juice company has its products viz. canned apple and bottled juice with profit margin Rs.4

and Rs.2 respectively per unit. The following table shows the labor, equipment, and ingredients

to produce each product per unit.

Canned Apple Bottled Juice Total

Labor 2 3 12

Equipment 3.2 1 8

Ingredients 2.4 2 9

Formulate the linear programming problem (model) specifying the product mix which will

maximize the profit without exceeding the levels of resourc

Answer 1

$\text{Let one unit of canned apple = x}\\\text{Let one unit of bottled juice = y}\\\text{z = 4x + 2y}\\\text{The constraint on labor is:}\\2x +3y\leq 12\\\text{The constraint on equipment is:}\\3.2x+y\leq 8\\\text{The constraint on ingredient is:}\\2.4x +2y\leq9 \\\text{Therefore the linear program is:}\\maximise: z=4x+2y\\\text{Subject to: }\\2x +3y\leq 12\\3.2x+y\leq 8\\2.4x +2y\leq9\\\text{with all variables non-negative}$