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 8 ounces of Colombian beans and 10 ounces of Brazilian beans. Coffee is shipped in 116-pound burlap bags. The company has 37 bags of Colombian beans and 44 bags of Brazilian beans on hand. How many pounds of each blend should they produce in order to use all the available beans?

To utilize all the available Colombian and Brazilian coffee beans, the coffee manufacturer should produce approximately 31.27 pounds of the mild blend and 234.52 pounds of the robust blend.

Explanation:

To utilize all the available Colombian and Brazilian coffee beans, the coffee manufacturer needs to determine the pounds of each blend to produce. Let's represent the pounds of the robust blend as R and the pounds of the mild blend as M. From the given information, we can set up the following system of equations:

R = 37 x 116 - 12M - 4R

M = 44 x 116 - 8M - 10R

To solve this system, we can use substitution or elimination method. Solving for R, we find that R = 7.5M. Plugging this value into the second equation, we get M = 31.27 pounds. Thus, the coffee manufacturer should produce approximately 31.27 pounds of the mild blend and 234.52 pounds of the robust blend to use all the available beans.

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