Resource allocation A coffee manufacturer uses Colombian and

Resource allocation. A coffee manufacturer uses Colombian and Brazilian coffee beans to produce two blends, robust and mild. A pound of the robust blend requires

12

ounces of Colombian beans and

4

ounces of Brazilian beans. A pound of the mild blend requires

6

ounces of Colombian beans and

10

ounces of Brazilian beans. Coffee is shipped in

95

-pound

burlap bags. The company has

36

bags of Colombian beans and

34

bags of Brazilian beans on hand. How many pounds of each blend should they produce in order to use all the available beans?

Robust.....?.... lbs

Mild....?.....lbs

Solution

Let a pound of Robust Blend = 12 C + 4 B where C = Colombian Beans and B = Brazilian Beans.

and a pound of Mild Blend = 6 C + 10 B.

Now, C = 36*95 = 3420

and B = 34*95 = 3230

Let x and y be the pounds of each blend they should produce in order to use all the available beans.

Then, R = 12x C + 4x B

and, M = 6y C + 10y B

From this we get,

12x + 6y = 3420 and 4x + 10y = 3230

Solving these liear equations for x and y, we get:

x = 154.375 and y = 261.25

Robust = 154.375

Mild = 261.25