MG1001 COURSEWORK 1 – Linear Programming;

A sports drink manufacturer is planning to introduce a new drink. The drink is made up entirely of 4 secret ingredients (A, B, C & D).

Each of the 4 ingredients contain different levels of 3 chemicals (X,Y,Z). Health regulations require that the dosage consumed per litre should contain minimum prescribed levels of chemicals X and Y and not exceed maximum prescribed levels for the third chemical (Z).

The composition of the 4 ingredients in terms of their chemical compounds (units per ml) is given in the table below, along with unit cost prices of the ingredients.

Additional requirements are that ingredient A should make up no more than 50% of the sports drink and there should be at least 100mL of ingredient B in every litre.

The company want to find the optimal way to mix the ingredients (A, B, C &D) to create 1 litre of the drink, at minimum cost.

Ingredient

Chemical

A

B

C

D

Requirements (units/litre)

X

3

4

8

10

At least 8,200

Y

5

3

6

6

At least 5,000

Z

10

25

20

40

At most 32,000

Cost per ml (p)

.2

.35

.3

.15

Formulate this problem as a Linear Programme, obtain an optimal solution and sensitivity report by using Solver. (50%)

Use this information to answer the following questions:

a) What is the minimum cost of producing a litre of the sports drink?

b) How much of each ingredient is included?

c) There is some uncertainty over the cost of ingredient C. How sensitive is the current optimal solution to this cost? Repeat this analysis for ingredient D.

d) Explain the practical implications of the shadow price for each of your constraints. (30%)

What advice would you give to the company? Give reasons for your recommendations and any reservations you have for their adoption in practice. (20%)

You should submit your formulation (with suitable explanations), the finished spreadsheet layout and the Solver sensitivity report and carefully explained answers to the questions above.