Ex 12.2, 8 A merchant plans to sell two types of personal computers – a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000. Let Number of Desktops be x,
Number of Portable Computers be y
According to Question :
Monthly demand of both items = maximum 250 Units
∴ x + y ≤ 250
Also,
Cost of Desktop = Rs 25000
Cost of Computers = Rs 40000
Max Investment = Rs 70,00,000
Hence,
25000 x + 40000 y ≤ 70,00,000
5x + 8y ≤ 1400
As we need to Maximize Profit,
Hence, Function Used here will be Maximize Z
Profit On Desktop → Rs 4500
Profit on Computers → Rs 5000
∴ Maximize Z = 4500 x + 5000y.
Combining all Constraints
Max Z = 4500 x + 5000y
Subject to Constraints
x + y ≤ 250
5x + 8y ≤ 1400
x ≥ 0 , y ≥ 0
Hence, the Profit will be maximum if company Produces : Number of Desktops → 200 Number of Portable Computers → 50 Max. Profit → Rs. 11,50,000

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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