Lpp Case Study

Case Studies - Linear Programming (LP)

1. Ms. Zeluah has started her own entrepreneurship. She designs, makes and sells trendy custom jewelries. As she is in the process of establishing herself in the jewelry market, for the time being she has restricted herself to only two types of jewelry – pendants and rings.

Each pendant needs 3 grams of gold and each ring needs 2.4 grams of gold. The labour-hours required for a pendant and a ring are 4 and 8 respectively. She has rationed herself to use a maximum of 24 grams of gold per day. She has also decided not to exceed a count of 40 labour-hours per day. There is always a daily demand for 2 pendants and the maximum of rings sold in one working day is 3.

Estimating that from each pendant she can make a profit of Rs 5000, and that from each ring Rs. 7000, she obviously wants to maximise her profits.

a) She now has changed her plan about labour-hours – the entire 40 labour-hours she hires per day has to be utilised, or else they will be have idle time.

b) Along with her new plans of labour-hours, she wants also to use up all 24 grams of gold she has rationed herself per day.

c) Added to the two changes stated above, she wants to make exactly 3 rings in one working day. She does alter the constraint about the market demand.

2. The emergency ward of a renowned hospital needs doctors round the clock. The 24 hours are broken into eight 3-hour time-spans. A doctor reports to the ward at the beginning of a time-span, stays there for 6 hours at a stretch and then leaves the ward at the end of the next time-span. Thus each doctor is available at the ward for exactly 6 hours; no doctor is permitted to stay beyond the stipulated 6 hours.

The time-spans and the required number of doctors in each span are given below.

Formulate this as an LPP so as to minimise the number of doctors to be recruited at the ward.

Time span | Minimum no. of doctors required |

6am-9am | 6 |

9am-12noon | 7 |...