Answer
3 ounces of Type I
Work Step by Step
Define Food Type I as x and Food Type II as y
With this, the objective function is stated to be $C = 0.2x + 0.3y$
The five equations you are given are:
$8x + 12y \geq 24$ for the fat
$12x + 12y \geq 36$ for the carbs
$2x + y \geq 4$ for the protein
$x + y \leq 5$ as the upper bound
and $x \geq 0 , y \geq 0$ for lower bounds
These give you the points, (0,4), (1,2), and (3,0)
When you plug these points back into the objective function, the costs for the mixtures are, 1.20 for (0,4), 0.80 for (1,2), and 0.6 for (3,0)
Since the problem asks you to find the cheapest option that still gives the mice all their nutrients the answer is (3,0) or 3 ounces of Type I
