the production planner for fine coffees, inc. produces two coffee blends: american (a) and british (b). two…

the production planner for fine coffees, inc. produces two coffee blends: american (a) and british (b). two of their resources are constrained: colombian beans, of which he can get at most 300 pounds (4,800 ounces) per week; and dominican beans, of which he can get at most 200 pounds (3,200 ounces) 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 dominican - bean constraint?\n\nmultiple choice\n\n12a + 8b ≤ 4,800\n\n8a + 12b ≤ 4,800\n\n4a + 8b ≤ 3,200\n\n8a + 4b ≤ 3,200

the production planner for fine coffees, inc. produces two coffee blends: american (a) and british (b). two of their resources are constrained: colombian beans, of which he can get at most 300 pounds (4,800 ounces) per week; and dominican beans, of which he can get at most 200 pounds (3,200 ounces) 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 dominican - bean constraint?\n\nmultiple choice\n\n12a + 8b ≤ 4,800\n\n8a + 12b ≤ 4,800\n\n4a + 8b ≤ 3,200\n\n8a + 4b ≤ 3,200

Answer

Explanation:

Step1: Identify resource and usage

The Dominican - bean resource is limited to 3200 ounces per week. An American blend coffee uses 8 ounces of Dominican beans per pound and a British blend coffee uses 4 ounces of Dominican beans per pound. Let (A) be the number of pounds of American blend and (B) be the number of pounds of British blend.

Step2: Formulate the constraint

The total amount of Dominican beans used for both blends must be less than or equal to the available amount. The amount of Dominican beans used for American blend is (8A) (8 ounces per pound of (A)) and for British blend is (4B) (4 ounces per pound of (B)). So the constraint is (8A + 4B\leq3200).

Answer:

8A + 4B ≤ 3200