1. Linear Program (2p.) A manufacturer wants to produce ice-cream. An ice-cream patch must contain at least 20 units of fat, at least 20 units of sugar, at least 1 unit of egg and at most 60 units of water. Below is a table of the raw ingredients available to the manufacturer, their compositions as percentages, and their prices.
Raw Cream Egg Whole Frozen sweetened glucose water ingredients yolk milk egg yolk syrup Fat 40 50 12 30 0 0 Sugar 0 0 0 14 70 0 Egg 0 40 0 40 0 0 Water 60 10 88 16 30 100 Price per unit 2 4 1 2 0.8 0
The goal of the manufacturer is to determine the recipe with minimum cost.
(a) (1p.) Write this problem as a linear program
(b) (1p.) Transform the linear program into the standard form. See the lecture script for the definition of the standard form.