Answer to Question #326619 in Operations Research for Fionna

Question

A veterinarian mixes two types of animal food: Food 1 and Food 2. Each unit of Food 1 cost P200 and contains 40 grams of fat, 30 grams of protein, and 1, 200 calories. Each unit of Food 2 cost P180 and contains 40 grams of fat, 60 grams of protein, and 1,600 calories. Suppose the veterinarian wants each unit of the final product to yield at least 360 grams of fat, at least 240 grams of protein and at least 9, 600 calories, how many grams of each of type of ingredients should the veterinarian use to minimize his cost?

Answer 1

$x_1-food\,\,1\\x_2-food\,\,2\\\left\{ \begin{array}{c} 40x_1+40x_2\geqslant 360\\ 30x_1+60x_2\geqslant 240\\ 1200x_1+1600x_2\geqslant 9600\\\end{array} \right. \\200x_1+180x_2\rightarrow \min \\Graphic\,\,method:\\x_1=0,x_2=9$

Indeed, we see that the level curves of the minimized function are more inclined to $x_1$ than the line $40x_1+40x_2\geq 360$

which means the minimum point is (0,9)