$1)($Baker and Powell, $2013)$ The Diaz Coffee Company blends three types of coffee beans $($Brazilian$,$ Colombian, and Peruvian$)$ into ground coffee to be sold at retail. Suppose that each kind of bean has a distinctive aroma and strength, and the company has a chief taster who can rate these features on a scale of $1$ to $100.$ The features of the beans are tabulated as follows:

Bean Aroma Rating Strength Rating Cost$/$lb$.$ Pounds Available

Brazilian $7515$ $$0\mathrm{.}501,500,000$

Colombian $6020$ $$0\mathrm{.}601,200,000$

Peruvian $8518$ $$0\mathrm{.}702,000,000$

The company would like to create a blend that has an aroma rating of at least $78$ and a strength rating of at least $16.$ Its supplies of the various beans are limited$,$ however. The available quantities are specified above. All beans are delivered under a previously arranged purchase agreement. Diaz wants to make four million pounds of the blend at the lowest possible cost.