Question

A small firm manufacturers gold rings and chains. The total number of rings and chains manufactured per day is atmost 24. It takes 1 hour to make a ring and 30 minutes to make a chain. The maximum number of hours available per day is 16. If the profit on a ring is Rs 300 and that on a chain is Rs 190, find the number of rings and chains that should be manufactured per day, so as to earn the maximum profit. Make it as an LPP and solve it graphically.

Answer 1

Total number of rings and chains manufactured per day = 24

Time taken in manufacturing ring = 1 hour

Time taken in manufacturing chain = 30 minutes

Time available per day = 16 hours

Maximum profit on ring = Rs 300

Maximum profit on chain = Rs 190

Let number of gold rings manufactured per day = x and chains manufactured per day = y

LPP is

Maximize Z = 300x + 190y ...(i)

Subject to constraints x ≥ 0, y ≥ 0 ...(ii)

x + y ≤ 24 ........(iii)

x + 12y ≤ 16 ......(iv)

Possible points for maximum Z are

A (0, 24), B (8, 16) and C (16, 0).

Z is maximum at (8, 16).

Hence, 8 gold rings and 16 chains must be manufactured per day.