Question 29 - CBSE Class 12 Sample Paper for 2018 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

A company produces two different products. One of them needs 1/4 of an hour of assembly work per unit, 1/8 of an hour in quality control work and Rs 1.2 in raw materials. The other product requires 1/3 of an hour of assembly work per unit, 1/3 of an hour in quality control work and Rs 0.9 in raw materials. Given the current availability of staff in the company, each day there is at most a total of 90 hours available for assembly and 80 hours for quality control. The first product described has a market value (sale price) of Rs 9 per unit and the second product described has a market value (sale price) of Rs 8 per unit. In addition, the maximum amount of daily sales for the first product is estimated to be 200 units, without there being a maximum limit of daily sales for the second product. Formulate and solve graphically the LPP and find the maximum profit.

This is a question of CBSE Sample Paper - Class 12 - 2017/18.

Question 29
A company produces two different products. One of them needs 1/4 of an hour of assembly work per unit, 1/8 of an hour in quality control work and Rs 1.2 in raw materials. The other product requires 1/3 of an hour of assembly work per unit, 1/3 of an hour in quality control work and Rs 0.9 in raw materials. Given the current availability of staff in the company, each day there is at most a total of 90 hours available for assembly and 80 hours for quality control. The first product described has a market value (sale price) of Rs 9 per unit and the second product described has a market value (sale price) of Rs 8 per unit. In addition, the maximum amount of daily sales for the first product is estimated to be 200 units, without there being a maximum limit of daily sales for the second product. Formulate and solve graphically the LPP and find the maximum profit.
Let Number of units of Product I produced be x,
Number of units of Product II produced be y
We need to maximize the Profit
Cost of Product I = Rs 1.2
Sale Price of Product I = Rs 9
Profit of Product I = Rs (9 – 1.2)
= Rs 7.8
Cost of Product II = Rs 0.9
Sale Price of Product II = Rs 8
Profit of Product II = Rs (8 – 0.9)
= Rs 7.1
∴ Z = 7.8x + 7.1y
Assembly Work
Time required on
Product I → 1/4 hour
Product II → 1/3 hour
Maximum Available Time = 90 hours
∴ 𝑥/4 + 𝑦/3≤ 90
(3𝑥 + 4𝑦)/12 ≤ 90
3x + 4y ≤ 1080
& x ≥ 0, y ≥ 0
Quality Control Work
Time required on
Product I → 1/8 hour
Product II → 1/3 hour
Maximum Available Time = 80 hours
∴ 𝑥/8 + 𝑦/3≤ 80
(3𝑥 + 8𝑦)/24 ≤ 80
3x + 8y ≤ 1920
& x ≥ 0, y ≥ 0
Also,
Maximum sales of first product is 200 units
∴ x ≤ 200
Combining all constraints :
Max Z = 7.8x + 7.1y
Subject to constraints,
3x + 4y ≤ 1080,
3x + 8y ≤ 1920
x ≤ 200,
& x ≥ 0 , y ≥ 0
Hence, profit will be maximum if
Number of Product I = 200
Number of Product II = 120
Maximum Profit = Rs. 2412

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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