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.

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:

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:

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.

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2