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  • Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 6

Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 6

Answers (1)

Answer:

Maximum profit =350

Deluxe model = 10

Ordinary model = 20

Hint:

Let required number of deluxe and ordinary model be x and y.

Given:

Since, Profit on each model of deluxe and ordinary type of Rs15 and Rs10 respectively.

Solution:

Let z be total profit then

z=15x+10y

Where x and y are required deluxe and ordinary model

Since each deluxe and ordinary model required 2 and 1 hour of skilled men, but twice available skilled men is 5×8 = 4 hours so,

2x+y\leq 40 (first constraint)

Given each deluxe and ordinary model require 2 and 3 hour of semi-skilled men, but total ratable by semi -skilled men is 100×8 = 80 hours so

2x+3y\leq 80 (second constraint)

Hence the required LPP

z =15x+10y

Subject to constraints

2x+y\leq 40

2x+3y\leq 80

x,y\geq 0,since number of ordinary model  cannot less than zero

The feasible region obtain by the system of constraint

Point (10,20) obtain by solving (i) and (ii).

The corner point of feasible region is O(0,0), A_{1}(20,0), P(0,20), B_{2}(0,40)

Corner Points

Value of z=15x+10y

O\left ( 0,0 \right )

0

A_{1}(20,0)

300

P(10,20)

350

B_{2}(0,40/3)

8003

Maximum z = 350 at x = 10, y = 20

Required number of deluxe model = 10 and required number of ordinary model = 20

Maximum profit  = 350

 

Posted by

infoexpert27

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