A coffee manufacturer uses Colombian and Brazilian coffee beans to produce two b

Question

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 122 -pound burlap bags. The company has 59 bags of Colombian beans and 29 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

Explanation / Answer

let they produce x pounds of robust blend

and y pounds of mild blend

columbian beans = 59 * 122 = 7198 pounds

brazilian beans = 29* 122 = 3538 pounds

lets form the equations from the information

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.

12 ounce = .75 pounds , 6 ounce = .375 pounds

.75x + .375 y = 7198

.25x + .625 y = 3538

solving equations for x and y

we get

x = 8458.66

y = 2277.33

therefore, they should produce robust blend = 8459 pounds and mild blend = 2277 pounds approximately

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