Question

A company produces two types of products say type A and B. Profits on the two types of product are Rs 30/- and Rs 40/- per kg respectively. The data on resources required and availability of resources are given below.

	Requirements		Capacity available per month
	Product A	Product B
Raw material (kgs)	60	120	12000
Machining hours/piece	8	5	600
Assembling (man hours)	3	4	500

Formulate this problem as a linear programming problem to maximize the profit.

Answer 1

(i) Variables: 

Let x₁ and x₂ denote the two types products A and B respectively.

(ii) Objective function: 

Profit on x₁ units of type A product = 30x₁ 

Profit on x₂ units of type B product = 40x₂ 

Total profit = 30x₁ + 40x₂ 

Let Z = 30x₁ + 40x₂, which is the objective function. 

Since the profit is to be maximized, we have to maximize Z = 30x₁ + 40x₂ 

(iii) Constraints: 

60x₁ + 120x₂ ≤ 12,000 

8x₁ + 5x₂ ≤ 600 

3x₁ + 4x₂ ≤ 500

(iv) Non-negative constraints: 

Since the number of products on type A and type B are non-negative, we have x₁, x₂ ≥ 0 

Thus, the mathematical formulation of the LPP is 

Maximize Z = 30x₁ + 40x₂ 

Subject to the constraints, 

60x₁ + 120x₂ ≤ 12,000 

8x₁ + 5x₂ ≤ 600 

3x₁ + 4x₂ ≤ 500 

x₁, x₂ ≥ 0