A firm produces three products. These products are processed on three different machines .The time required to manufacture one unit of each of the three products and the daily capacity of the three machines are given in the table below :
Machine
Time per unit Product 1
Time per unit Product 2
Time per unit Product 3
Machine capacity
M 1
2
3
2
440
M 2
4
_
3
470
M 2
2
5
_
430

It is required to determine the daily number of units to be manufactured for each product. The profit per unit for product 1,2 and 3 is Rs 4 , Rs. 3 and Rs 6 respectively .If it is assumed that all the amounts produced are consumed in the market .
State True or False:
Subject to constraints , 2n1 +3n2+2n3 ≤ 440
4n1 +3n3 ≤ 470
2n1 + 5n2 ≤ 430

Question

A firm produces three products. These products are processed on three different machines .The time required to manufacture one unit of each of the three products and the daily capacity of the three machines are given in the table below :
Machine
Time per unit Product 1
Time per unit Product 2
Time per unit Product 3
Machine capacity
M 1
2
3
2
440
M 2
4
_
3
470
M 2
2
5
_
430

It is required to determine the daily number of units to be manufactured for each product. The profit per unit for product 1,2 and 3 is Rs 4 , Rs. 3 and Rs 6 respectively .If it is assumed that all the amounts produced are consumed in the market .
State True or False:
Subject to constraints , 2n1 +3n2+2n3 ≤ 440
4n1 +3n3 ≤ 470
2n1 + 5n2 ≤ 430

Accepted Answer

The above statement is true.Step 1The number of units of products 1,2 and 3 to be produced dailyStep 2The numbers of units of products 1,2 and 3 manufactured daily are n1 ,n2 and n3 .Step 3Values of x1,x2 and x3 Where n1,n2 ,n3 ≥OSince ,negative production has no meaning and is not feasible . Step 4The present situation, objective is to maximize the profit Maximise Z = 4n1+3n2+6n3Step 5Here , constraints are on the machine capacities and can be mathematically expressed as 2n1+3n2+ 2n3 ≤ 4404n1+0.n2 +3n3 ≤ 4702n1 + 5n2+0.n3≤ 430The complete mathematical model for the problem can be written as Maximize Z = 4n1 +3n2 +6n3Subject to constraints ,2n1 +3n2+2n3 ≤ 4404n1 +3n3 ≤ 4702n1 + 5n2 ≤ 430

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Machine	Time per unit Product 1	Time per unit Product 2	Time per unit Product 3	Machine capacity
M 1	2	3	2	440
M 2	4	_	3	470
M 2	2	5	_	430