CBSE Class 12 · 2010 · Linear ProgrammingLong Answer

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A small firm manufactures gold rings and chains. The total number of rings and chains manufactured per day is at most 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 L.P.P. and solve it graphically.

Answer: Max profit = Rs 5440 at (8, 16): 8 rings and 16 chains

Solution

Let

x

gold rings and

y

chains be made per day.
Profit:

Z = 300 x + 190 y

.
Total number:

x + y \leq 24

Time:

x + \frac{1}{2} y \leq 16 ⟹ 2 x + y \leq 32

x \geq 0, y \geq 0

Corner points:

(0, 0)

(16, 0)

(8, 16)

(intersection of

x + y = 24

and

2 x + y = 32

) and

(0, 24)

.
Evaluate

Z = 300 x + 190 y

(16, 0)

Z = 4800

(8, 16)

Z = 2400 + 3040 = 5440

← maximum

(0, 24)

Z = 4560

∴ Z_{m a x} = Rs 5440 at (8, 16)

8 gold rings and 16 chains should be manufactured per day.

Structure Feasible region for x + y = 24 and x + y/2 = 16, with corner points (0, 24), (8, 16) and (16, 0). — Feasible region for x + y = 24 and x + y/2 = 16, with corner points (0, 24), (8, 16) and (16, 0).

CBSE Class 12 Board · 2010 · Subjective

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CBSE Class 12 · 2010 · Linear ProgrammingLong Answer

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