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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.
Solution
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 Totat profit
z= 5x + 6y
\[3x + 2y \leq 130\]
\[4x + 6y \leq 260\]
\[x \geq 0, y \geq 0\]
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