Management Summary Mike O'Sullivan, 1234567
Problem Summary
Uncle Ben’s want to produce their cat food products as cheaply as possible while ensuring they meet the stated nutritional analysis requirements shown on the cans. Thus they want to vary the quantities of each ingredient used (the main ingredients being chicken, beef, mutton, rice, wheat and gel) while still meeting their nutritional standards.
The stated nutritional analysis requirements are:

The % of Crude Protein must be at least 8%.

The % of Crude Fat must be at least 6%.

The % of Crude Fibre must be at most 2%.

The % of (Naturally Occurring) Salt must be at most 0.4%.
They are producing 100g cans, so the nutritional requirements correspond to:

At least 8g of Protein.

At least 6g of Fat.

At most 2g of Fibre.

At most 0.4g of (Naturally Occurring) Salt.
The cost for each ingredient is given in Table 1.
Ingredient

Cost (per g)

Chicken

$0.013

Beef

$0.008

Mutton

$0.010

Rice

$0.002

Wheat

$0.005

Gel

$0.001

Table 1 Cost of the ingredients
To find the right mix of ingredients we formulated this problem as a linear programme in AMPL (see www.ampl.com for details) and solved it with the CPLEX (see www.cplex.com for details) solver.
Results
With the current input data, the optimal solution is shown in Table 2. The time to find this solution was negligible.
Ingredient

Optimal amount (g)

Chicken

0

Beef

60

Mutton

0

Rice

0

Wheat

0

Gel

40

Table 2 Optimal mix of ingredients
To minimise the cost per 100g can of Whiskas cat food, Whiskas should use
The cost per can is $0.52 or 52c. 