(a) Formulate this problem to find the best combination of the two supplements to meet the minimum requirements at the least cost.

(b) Solve for the optimal solution by the simplex method.

- Thread starter mitchfel
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(a) Formulate this problem to find the best combination of the two supplements to meet the minimum requirements at the least cost.

(b) Solve for the optimal solution by the simplex method.

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The required info from the text in a nutshell are:

Now I introduce the variables \(\displaystyle x\) (product A) and \(\displaystyle y\) (product B) and enter the information into a table.

Product A | Product B | Amount in mixture | |

protein | 1 | 2 | 30 |

riboflavin | 1 | 4 | 80 |

price | 9 | 15 |

My objective function now would be the cost minimization, so something like \(\displaystyle z(x,y) = 9x+15y \quad\text{(min)}\).

Now it is clear from the text that

\(\displaystyle 1x+2y \geq 30\)

\(\displaystyle 1x+4y \geq 80\)

In addition we accept only positive values for \(\displaystyle x\) and \(\displaystyle y\), so:

\(\displaystyle x \geq 0\)

\(\displaystyle y \geq 0\)

I had it all plotted once and saw that the intersection of the products is in the negative range (\(\displaystyle S=(-20|25)\)), this confuses me (or I don't know how to interpret this). What do you say to the approach, any suggestions?