Question

The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). Two of his resources are constrained: Columbia 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 10 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 6 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 are optimal weekly profits?

Answer 1

If it is assumed that X₁ and X₂ are the number pounds of American blend and British blend coffee respectively

The profits need to be maximised so

objective function OF = Maximise (2X₁+X₂)

subject to constraints

10X₁+6X₂ <=4800

4X₁+6X₂ <=3200

and X₁, X₂ =>0

From the equations, the points of optimality are (480,0) (0,533) and ( 266.66,355.55)

Value of OF on the three points

at point 1 = 2x480 +0=960

at point 2 = 0+533.33 =533.33

at point 3 = 2x266.6+355.55 =888.75

The maximum profit is obtained at (480,0) which is 960.