Task 5: Linear programming

Tragani switched some of the production at the Argyll factory over to making gowns – a vital component of personal protective equipment (PPE) during the pandemic. Four different sizes of gown are to be manufactured: Small (S), Medium (M), Large (L) and Extra Large (X).

The manufacture of the gowns involves:

• laying pattern pieces in the most efficient way possible,
• cutting the pieces,
• machining
• and finally wrapping in packs of 10 for distribution.

The company’s staff work 35hr weeks and they have decided to dedicate the following staff to PPE production: 15 Machinists, One pattern layer and cutter and 10 hours of packing time.

All gowns require 30 minutes of machining and it takes 4 minutes to wrap into packs of 10 for distribution. Extra Large gowns require slightly longer than other sizes to layout and cut at 7 minutes with the other sizes taking 5 minutes.

The company’s aim is to produce at least 50 each of the Small, Medium and Large sizes and at least 30 Extra Large. However, they have also been informed that they will need no more than 50 extra-large and 150 small gowns. There is 1500m of material available for production, but the company wishes to also maximise the amount PPE production i.e. material used. The material required for each item being 2.5m for Small, 2.6m for Medium, 2.9m for Large and 3m for Extra Large

In preparation for the examination you are asked to use the linear programming technique (known as Data Solver on Excel) to assist the company in determining how many of the four different products to produce per week.

When undertaking the linear programming, please ensure you request a sensitivity report as part of the solution.

The results and sensitivity report you have produced will be referred to in the examination that takes place at the end of the semester. Therefore, it is vital that you print out the completed work, add any extra notes you may find useful and bring these to the examination with you.