$1.$ A linear programming computer package is needed.

Hilltop Coffee manufactures a coffee product by blending three types of coffee beans. The cost per pound and the available pounds of each bean are as follows.

Bean Cost per Pound Available Pounds

$1$ $$0\mathrm{.}50450$

$2$ $$0\mathrm{.}70650$

$3$ $$0\mathrm{.}45450$

Consumer tests with coffee products were used to provide ratings on a scale of $0100,$ with higher ratings indicating higher quality. Product quality standards for the blended coffee require a consumer rating for aroma to be at least $75$ and a consumer rating for taste to be at least $80.$ The individual ratings of the aroma and taste for coffee made from $100\%$ of each bean are as follows:

Bean Aroma Rating Taste Rating

$17585$

$28587$

$36074$

Assume that the aroma and taste attributes of the coffee blend will be a weighted average of the attributes of the beans used in the blend.