Problem 1
A bakery has 50 kg of flour, 1.5 kg of meat, 6 kg of sugar and 5 kg of butter. Each loaf of bread uses 300 g of flour and 10 g of sugar, and yields a profit of $0.25. Each pie uses 80 g of flour, 60 g of meat, 10 g of sugar and 40 g of butter, and yields a profit of $0.15. Each cake uses 250 g of flour, 200 g of sugar and 150 g of butter, and yields a profit of $0.70. Formulate the problem to determine how many loaves of bread, pies and cakes the bakery should produce to maximise profit.
Problem 2
An advertising campaign must reach 50% of the 15–24-year-old market, 40% of the 25–34-year-old market and 20% of the 35–44-year-old market. Each thousand dollars spent in cinema advertising reaches 2% of the 15–24 market, 1.5% of the 25–34 market and 1% of the 35–44 market. Each thousand dollars spent in TV advertising reaches 2% of the 15–24 market, 1% of the 25–34 market and 1.5% of the 35–44 market. Each thousand spent on newspaper advertising reaches 0.5% of the 15–24 market, 1.5% of the 25–34 market and 2% of the 35–44 market. Formulate the problem to minimise the total cost of the advertising campaign.