Resource allocation. A coffee manufacturer uses Colombian and Brazilian coffee b

Question

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 125pound burlap bags. The company has 40 bags of Colombian beans and 37 bags of Brazilian beans on hand. How many pounds of each blend should they produce in order to use all the available beans?

Robustequals = lbs

Mildequals= lbs

(Round each answer to the nearest pound.)

Explanation / Answer

Given data:

There are two types of coffee beans Colombian and Brazilian which are used to produce two blends called robust and mild.

One pound(1lb) of the robust blend requires 12 ounces of Colombian beans and 4 ounces of Brazilian beans.

similarly, one pound(1lb) of the mild blend requires 6 ounces of Colombian beans and 10 ounces of Brazilian beans.

one bag size is 125 pounds(lbs) and company has 40 bags of Colombian beans and 37 bags of Brazilian beans.

procedure:

As one pound = 16 ounce

one bag size = 125*(16 ounce) = 2000 ounce

That implies,

Size of 40 bags of Colombian beans = 40*(2000 ounce) = 80000 ounce

Size of 37 bags of Brazilian beans = 37*(2000 ounce) = 74000 ounce

Assume there are 'R' pounds(lbs) of Robust blend and 'M' pounds(lbs) of Mild blend

As one pound of robust blend requires 12 ounces of Colombian beans and one pound of mild blend requires 6 ounce of Colombian beans,

The equation should be

12*R+6*M=80000 -------(1)

similarly for Brazilian beans, the equation is

4*R+10*M=74000 --------(2)

multiply equation (2) with constant 3 =>

12*R+30*M=222000 -------(3)

subtract (1) from (3)

we get, 24*M=142000 => M = (17750/3) = 5916.667

Now, substitute M= (17750/3) in (1)

=> R = (11125/3) = 3708.333

Finally, answer is

Robustequals= 5917 lbs

Mildequals= 3708 lbs

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