Question

A firm manufactures two products, each of which must be processed through two departments, 1 and 2. The hourly requirements per unit for each product in each department, the weekly capacities in each department, selling price per unit, labour cost per unit, and raw material cost per unit are summarized as follows:

	Product A	Product B	Weekly capacity
Department 1	3	2	130
Department 2	4	6	260
Selling price per unit	₹ 25	₹ 30
Labour cost per unit	₹ 16	₹ 20
Raw material cost per unit	₹ 4	₹ 4

The problem is to determine the number of units to produce each product so as to maximize total contribution to profit. Formulate this as a LPP.

Answer 1

The given data can be arranged in the following tabular form:

	Product A	Product B	Weekly capacity
Department 1	3	2	130
Department 2	4	6	260

	Product A	Product B
Selling price per unit	Rs 25	Rs 30
Labour cost per unit	Rs 16	Rs 20
Raw material cost per unit	Rs 4	Rs 4

Let $x$ be the number of units of product A.
Let $y$ be the number of units of product B.
Profit per unit$=$Selling price per unit$-$Labour cost per unit$-$Raw material cost per unit
Profit on one unit of product A$=25-16-4=$Rs$5$
Profit on one unit of product B$=30-20-4=$Rs $6$
Total profit, $Z=5x+6y$
According to the question,
$$\begin{gathered} 3x+2y\le 130 \\ 4x+6y\le 260 \\ x\ge 0,y\ge 0 \end{gathered}$$