a coffee manufacturer uses columbian and brazilian coffee beans to produce two b

Question

a coffee manufacturer uses columbian 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. coffe is shipped in 101-pound burlap bags. the company has 51 bags of colombian beans and 31 bags of brazilian beans on hand. how many pounds of each blend should they produce in order to use all the available beans?

Explanation / Answer

1)
Let the ratio be x :(1-x). Then,
14.6x + 9.8(1-x) = 11(x+(1-x))
14.6x + 9.8(1-x) = 11
4.8x = 1.2
x = 0.25
The ratio is 0.25 : 0.75

2)
Let x pounds of robust and y pounds of mild be the quantity produced.
Total requirements is 132x90 = 11880.

colambeam bean available = 132x50 = 6600
Brazilian beans available = 132x40 = 5280
Then,
x+y = 11880
0.75x+0.375y = 6600
0.25x+0.625y = 5280
Solving equation x= -5720 y =-6160

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