Step 1

Only A and B part.

X= Ounces of Oats

Y= Ounces of Rice

\(\displaystyle{8}{X}+{6}{Y}\geq{48}\) vitamin A

\(\displaystyle{1}{X}+{2}{Y}\geq{12}\) vitamin B

\(\displaystyle{\cos{{t}}}={0.05}{X}+{0.03}{Y}\)

Step 2

The critical values are on the graph

The costs at each critical value are as follows:

\(\displaystyle{C}{\left({0},{8}\right)}={0.05}{\left({0}\right)}+{0.03}{\left({8}\right)}=\${0.24}\)

\(\displaystyle{C}{\left({2.4},{4.8}\right)}={0.05}{\left({2.4}\right)}+{0.03}{\left({4.8}\right)}=\${0.264}\)

\(\displaystyle{C}{\left({12},{0}\right)}={0.05}{\left({12}\right)}+{0.03}{\left({0}\right)}=\${0.60}\)

So the minimum cost occurs when 8 ounces of rice are used and zero ounces of oats are used.

Minimum \(\displaystyle{\cos{{t}}}=\${0.24}\)

Only A and B part.

X= Ounces of Oats

Y= Ounces of Rice

\(\displaystyle{8}{X}+{6}{Y}\geq{48}\) vitamin A

\(\displaystyle{1}{X}+{2}{Y}\geq{12}\) vitamin B

\(\displaystyle{\cos{{t}}}={0.05}{X}+{0.03}{Y}\)

Step 2

The critical values are on the graph

The costs at each critical value are as follows:

\(\displaystyle{C}{\left({0},{8}\right)}={0.05}{\left({0}\right)}+{0.03}{\left({8}\right)}=\${0.24}\)

\(\displaystyle{C}{\left({2.4},{4.8}\right)}={0.05}{\left({2.4}\right)}+{0.03}{\left({4.8}\right)}=\${0.264}\)

\(\displaystyle{C}{\left({12},{0}\right)}={0.05}{\left({12}\right)}+{0.03}{\left({0}\right)}=\${0.60}\)

So the minimum cost occurs when 8 ounces of rice are used and zero ounces of oats are used.

Minimum \(\displaystyle{\cos{{t}}}=\${0.24}\)