Answer to Question #326620 in Operations Research for Fionna

Question

A hog raiser is mixing two types of grains A and B. each units of grain A costs P50 and contains 20 grams of fat and 10 grams of protein. Each unit of grain B costs P80 and contains 30 grams of fat and 30 grams of proteins. The hog raise wants each units of the final product to yield at least 180 grams of fat and at least 120 grams of protein. How many units of each type of grain should he use to maximize his sales?

Answer 1

$x_1-A\\x_2-B\\\left\{ \begin{array}{c} 20x_1+30x_2\geqslant 180\\ 10x_1+30x_2\geqslant 120\\\end{array} \right. \\50x_1+80x_2\rightarrow \min \\Graphic\,\,method:\\The\,\,inter\sec tion\,\,point\\\left\{ \begin{array}{c} 20x_1+30x_2=180\\ 10x_1+30x_2=120\\\end{array} \right. \Rightarrow \left\{ \begin{array}{c} 2x_1+3x_2=18\\ x_1+3x_2=12\\\end{array} \right. \Rightarrow \left\{ \begin{array}{c} x_1=6\\ x_2=2\\\end{array} \right.$