# A factory produces plastic components for a car company

A factory produces plastic components for a car company

BE310 Assignment Group 1. A factory produces plastic components for a car company. The table below shows the length of time (in minutes) it takes to carry out each of the processes on each of the components.

## BE310 A factory produces plastic components for a car company

(1) BE310 A factory produces plastic components for a car company. It makes three types; A, B and C. The table below shows the length of time (in minutes) it takes to carry out each of the processes on each of the components. The column on the right gives the total production time (in minutes) that can be allocated to each of the processes over the next production period. [50 marks]

Process Type Total production time for

A B C each process (minutes)

Moulding 6 12 8 81000

Trimming 4 4 6 32400

Packaging 3 2 3 16300

Each component of type A makes a profit of £12 for the factory. Similarly, each component of type B makes a profit of £16, and each component of type C makes a profit of £13.

Firstly, Prepare a report for the factory management.

Secondly, Your report should include:

a) The above problem formulated as a linear programming problem. [20 marks]

b) The use of Excel to work out the amounts of each type of component that should be produced to maximise profits, whilst satisfying the constraints. [20 marks]

c) The maximum profit which will therefore be gained. [5 marks]

d) Comments about whether any production time remains unused at the end of the production period. [5 marks]

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**Question two**

(2) [50 marks] Firstly, EDCF is a company selling cheap wall clocks. Their selling price is £20 per wall clock. They can either manufacture the wall clocks at their own plant in theUK or import them.

Moreover, If the company decides to import the wall clocks, there is a 40% chance that a tariff of £2 per wall clock will be imposed. The company will only find out whether there is a tariff after they have made the decision to import or manufacture the clocks.

Additionally, It may be assumed that the demand for wall clocks in a day will either be 200 or 300. If it is 200, it costs EDCF £14 per wall clock to manufacture and £13 per clock to import.

Besides, If the demand is 300, it costs EDCF £10 per clock to manufacture and £9 per clock to import.

Further, EDCF has also the option to advertise the product each day. If they do advertise on a particular day, it costs them £800, and there is a 75% chance that the demand will be 300 wall clocks (and a 25% chance that it will be 200).

Also, If they choose not to advertise, there is a30% chance that the demand will be 300 clocks and a 70% chance it will be 200.

Lastly, Use Excel to construct a Decision Tree for this problem.

Finally, Use it to determine EDCF’s optimal decisions about manufacturing, importing and advertising of the wall clocks.

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