Question

For a given week, Heather's Coffee House has available 600 ounces of A grade coffee and 875 ounces of B grade coffee. These are blended into packages as follows: a deluxe blend that contains 3 ounces of A grade coffee and 7 ounces of B grade coffee, and a special blend that contains 4 ounces of A grade coffee and 5 ounces of B grade coffee. Let x be the number of deluxe blend packages sold. Let y be the number of special blend packages sold. Shade the region corresponding to all values of x and y that satisfy these requirements.

Answer 1

To determine the region that satisfies the requirements, set up inequalities using the available quantities of A and B grade coffee. Graph the shaded region that satisfies both inequalities.

Step-by-step explanation:

To shade the region corresponding to all values of x and y that satisfy the given requirements, we need to set up inequalities using the available quantities of A and B grade coffee. Let's denote the number of deluxe blend packages sold as x and the number of special blend packages sold as y.

From the information given, we know that each deluxe blend package contains 3 ounces of A grade coffee and 7 ounces of B grade coffee, and each special blend package contains 4 ounces of A grade coffee and 5 ounces of B grade coffee.

So, for the quantity of A grade coffee:

3x + 4y ≤ 600 (since the total quantity of A grade coffee cannot exceed 600 ounces)

And for the quantity of B grade coffee:

7x + 5y ≤ 875 (since the total quantity of B grade coffee cannot exceed 875 ounces)

By graphing the shaded region that satisfies both of these inequalities, we can determine the values of x and y that meet the requirements.

Answer 2

Shaded area in the graphic attached.

Step-by-step explanation:

Let x be the number of deluxe blend packages sold.

Let y be the number of special blend packages sold.

We can write the restrictions for A and B as:

Restriction for A: the deluxe package needs 3 ounces per package and the special package needs 4 ounces per package.

The total amount of A available is 600 ounces.

We can express that as:

`3x+4y\leq600`

Restriction for B: the deluxe package needs 7 ounces per package and the special package needs 5 ounces per package.

The total amount of B available is 875 ounces.

We can express that as:

`7x+5y\leq875`

This two restictions can be graphed and shade the feasible region, that is the region defined by A and B restrictions plus the non-negative restriction (x,y > 0).

The graph is attached.