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.

Asked by Sakshi | 1 year ago | 50

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,

3x+2y≤130

4x+6y≤260

x≥0, y≥0

Answered by Aaryan | 1 year agoMinimize Z = 2x + 4y

Subject to

x+y≥8

x+4y≥12

x≥3, y≥2

Maximize Z = 7x + 10y

Subject to

x+y≤30000

y≤12000

x≥6000

x≥y

x, y≥0

Maximize Z = 10x + 6y

Subject to

3x+y≤122x+5y≤34 x, y≥0

Maximize Z = 15x + 10y

Subject to

3x+2y≤802x+3y≤70 x, y≥0