Answer to Question #321142 in Operations Research for Dama

Question

Tigist wishes to mix two types of food C and D in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin C and 11 units of vitamin D. Food C costs $ 60/kg and Food D costs $80/kg. Food C contains 3 units/kg of Vitamin A and 5 units / kg of Vitamin B while food D contains 4 units/kg of Vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture by graphic model.

Answer 1

$x_1-mass\,\,of\,\,food\,\,C\\x_2-mass\,\,of\,\,food\,\,D\\\left\{ \begin{array}{c} 3x_1+4x_2\geqslant 8\\ 5x_1+2x_2\geqslant 11\\\end{array} \right. \\Z=60x_1+80x_2\rightarrow \min \\We\,\,see\,\,from\,\,the\,\,graph\,\,that\,\,\min imum\,\,is\,\,for\\\left\{ \begin{array}{c} 3x_1+4x_2=8\\ 5x_1+2x_2=11\\\end{array} \right. \Rightarrow x_1=2,x_2=0.5\\Z_{\min}=60\cdot 2+80\cdot 0.5=160$