Introducing your new favourite teacher - Teachoo Black, at only ₹83 per month

Manufacturing problems

Example 8
Deleted for CBSE Board 2023 Exams

Ex 12.2, 3 Important Deleted for CBSE Board 2023 Exams

Ex 12.2, 4 Important Deleted for CBSE Board 2023 Exams

Ex 12.2, 5 Deleted for CBSE Board 2023 Exams

Ex 12.2, 6 Deleted for CBSE Board 2023 Exams

Ex 12.2, 7 Important Deleted for CBSE Board 2023 Exams You are here

Misc 4 Important Deleted for CBSE Board 2023 Exams

Misc 10 Important Deleted for CBSE Board 2023 Exams

Example 10 Deleted for CBSE Board 2023 Exams

Last updated at Feb. 17, 2020 by Teachoo

Ex 12.2, 7 A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximise the profit?Let the number of souvenirs of type A be x and number of souvenirs of type B be y Cutting Type A requires → 5 min Type B requires → 8 min Maximum Time = 200 min ∴ 5x + 8y ≤ 200 Assembling Type A requires → 10 min Type B requires → 8 min Maximum Time = 240 min ∴ 10x + 8y ≤ 240 As, we need to maximize the profit, so the function used here will be Maximize z. Profit on Type A → Rs. 5 Profit on Type B → Rs. 6∴ Maximize z = 5x + 6y Combining all Constraints : Maximize Z = 5x + 6y Subject to Constraints : 5x + 8y ≤ 200 10x + 8y ≤ 240 x ≥ 0 , y ≥ 0 Hence, Profit will be maximum if company Produces 8 souvenirs of type A and 20 Souvenirs of Type B Max. Profit = Rs.160