Question

The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound.

What is the constraint for Colombian beans?

A + 2B ? 4,800

12A + 8B ? 4,800

2A + B ? 4,800

8A + 12B ? 4,800

4A + 8B ? 4,800

Answer 1

12A + 8B ≤ 4800

Explanation:

Here A represents the number of pounds of american blend and B represents the number of pounds of British blend,

Now, each pounds of american blend produced 12 ounces of colombian beans,

So, the total colombian beans from american blend = 12A

Also, each pounds of British blend produced 8 ounces of colombian beans,

So, the total colombian beans from british blend = 8B

⇒ Total colombian beans = 12A + 8B

∵ Total Colombian beans is at most 300 pounds or 4800 ounces ( 1 pound = 16 ounces )

⇒ 12A + 8B ≤ 4800

∵ Constraint shows the limitation or restriction of a thing.

Hence, the constraint for Colombian beans ( that shows its limitation of quantity ),

12A + 8B ≤ 4800