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 91 ​-pound burlap bags. The company has 63 bags of Colombian beans and 28 bags of Brazilian beans on hand. How many pounds of each blend should they produce in order to use all the available​ beans?

a) Robust = 35 lbs, Mild = 28 lbs
b) Robust = 28 lbs, Mild = 35 lbs
c) Robust = 21 lbs, Mild = 42 lbs
d) Robust = 42 lbs, Mild = 21 lbs

Answer 1

To use all the available beans, the company should produce 42 pounds of the robust blend and 21 pounds of the mild blend.

Step-by-step explanation:

To use all the available beans, we need to determine the maximum number of pounds of Colombian and Brazilian beans that can be used.

Let's start by finding the number of pounds of Colombian beans available. We are given that there are 63 bags of Colombian beans, and each bag weighs 91 pounds. So the total weight of Colombian beans available is 63 bags * 91 pounds per bag = 5733 pounds.

Next, we find the number of pounds of Brazilian beans available. We are given that there are 28 bags of Brazilian beans, and each bag weighs 91 pounds. So the total weight of Brazilian beans available is 28 bags * 91 pounds per bag = 2548 pounds.

Now, let's determine the number of pounds of each blend that can be produced. For the robust blend, each pound requires 12 ounces of Colombian beans and 4 ounces of Brazilian beans. Since 1 pound is equal to 16 ounces, we can write the proportion: 12 ounces Colombian beans / 4 ounces Brazilian beans = X pounds Colombian beans / 1 pound robust blend. Solving for X, we find that X = 3 pounds of Colombian beans.

Similarly, for the mild blend, each pound requires 6 ounces of Colombian beans and 10 ounces of Brazilian beans. Using the same proportion method, we find that X = 5 pounds of Brazilian beans.

Therefore, the company should produce 3 pounds of the robust blend and 5 pounds of the mild blend in order to use all the available beans. So the correct answer is option d) Robust = 42 lbs, Mild = 21 lbs.