Posted by Rachel | Posted in Coffee and Accessories | Posted on 07-04-2010
Tags: bag, bags, burlap, burlap coffee bags for sale, burlap coffee bean bags, burlap-bag, coffee, coffee bags burlap, coffee bags burlap pillows, used coffee bags burlap
linear maximization (math)?
a coffee manufacturer uses columbian and brazilian coffee beans to produce two blends, robust and mild. a pound of robust requires 12 ounces of columbian and 4 ounces of brazilian. a pound of the mild blend requires 6 ounces of columbian and 10 ounces of brazilian. coffee is shipped in 133 pound burlap bags. the company has 65 bags of columbian and 34 bags of brazilian on hand. how many pounds of each blend (robust and mild) should they produce in order to use all available beans?
65 bags of columbian –> 65*133*16 = 138,320 oz of columbian beans
34 bags of brazilian –> 34*133*16 = 72,352 oz of brazilian beans
robust = 12c + 4b and mild = 6c + 10b
We need to find limiting conditions.
If you make all robust, you will make
max[(138320/12),(72352/4)] –> 11526 pounds. By making that amount, you wind up having
138320-11526(12) = 80 oz of columbian left over and 72352-4(11526) = 26248 oz brazilian, for a total of 26328 oz beans left over.
If you make only mild, you will make 7235 pounds but will have 94912 oz of beans left over (I’ll leave the check of that to you).
Even if you decide to make a pound of each and figure out the limiting condition, you will be able to make 5168 pounds of each and be left with 45296 oz of total beans.
Therefore, to use the most beans you should make all robust –> 11526 lbs of robust, leaving 80 oz of columbian and 26248 oz of brazilian.
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