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$$$0\mathrm{.}504502$$$0\mathrm{.}705503$$$0\mathrm{.}45350$

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 $175872858936074$

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.

$($a$)$

What is the minimum$-$cost blend $($in pounds$)$ that will meet the quality standards and provide $1,000$ pounds of the blended coffee product?

Bean $1$ lb Bean $2$ lb Bean $3$ lb

$($b$)$

What is the cost per pound for the coffee blend $($in dollars$)?$

$

$($c$)$

Determine the aroma rating for the coffee blend.

Determine the taste rating for the coffee blend.

$($d$)$

If additional coffee were to be produced, what would be the expected cost per pound $($in dollars$)?$

$