A confectioner sells two types of nut mixtures. The standard-mixture package contains 100 g of cashews and 200 g of peanuts and
sells of $1.95. The deluxe-mixture package contains 150 g of cashews and 50 g of peanuts and sells for $2.25. The confectioner
has 15 kg of cashews and 20 kg of peanuts available. On the basis of past sales, the confectioner needs to have at least as many
standard as deluxe packages available. How many bags of each mixture should she package to maximize her revenue?
For this problem we will let represent the number of standard-mixture packages and let represent the number of deluxe-mixtuer packages. The values of and that will maximize her revenue depend on the amount of cashews and peanuts available for use. These are known as constraints as they constrain the possible values of the variables 1. There are 15 kg of cashews available and since the standard-mixture uses 100 g and the deluxe-mixture uses 150 g we must make sure that
100x+150y<15,000 ⇒ 2x+3y<300