Decision Variables: Algebra / Calculations

Decision Variables: Algebra / Calculations

Construct a mathematical model for this problem. In doing so, consider the following:
(a) What are the decision variables for this problem?
(1 Mark)
(b) Using decision variables identified in part (a), formulate the objective
function for this problem. Is the quantity of interest to be maximised or
minimised?
( 2 Marks)
(c) What constraints are relevant to this problem? Using the decision variables
from part (a), formulate those constraints.
(5 Marks)

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Dean runs The Creamy Bar which specialises in artisan ice cream sold at a local farmer’s
market. Prevailing prices in the local market are $10 for a take-home tub of Classic Vanilla
and $18 for a tub of Chocolate Almond Fudge.
The local dairy farmer delivers 50 litres of milk every Friday in preparation for market day.
Classic Vanilla will need 0.5 litres per tub and Chocolate Almond Fudge requires 3 times
as much. Both flavours require 500g of sugar to enhance the taste. There is a total of
22kg of sugar available per market day. For the signature velvety mouthfeel, Dean adds
0.5 litres of heavy cream to Classic Vanilla and double the amount for Chocolate Almond
Fudge. He ordered 55 litres of heavy cream from the supplier.

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