A small firm makes three products, which all follow the same three-step process,

Question

A small firm makes three products, which all follow the same three-step process, which consists of milling, inspection, and drilling. Product A requires 6 minutes of milling, 5 minutes of inspection, and 4 minutes of drilling; product B requires 2.5 minutes of milling, 2 minutes of inspection, and 2 minutes of drilling; and product C requires 5 minutes of milling, 4 minutes of inspection, and 8 minutes of drilling. The department has 20 hours available during the next period for milling, 15 hours for inspection, and 24 hours for drilling. Product A contributes $6.00 per unit to profit, product B contributes $4.00 per unit, and product C contributes $10.00 per unit.

The following is the output maximizing profits for the next period:

PROBLEM TITLE: LINEAR PROGRAMMING
PROBLEM IS A MAX WITH 3 VARIABLES AND 3 CONSTRAINTS.

NUMBER OF ITERATIONS: 2
OPTIMAL SOLUTION:
OBJECTIVE FUNCTION VALUE = 2,070
DECISION VARIABLE SECTION:

SLACK VARIABLES SECTION:

What would the objective function value be if 3 more units of each X4, X5, and X6 were added assuming they are within the range of optimality?

Explanation / Answer

As per given requirement the production planner for Fine Coffees, Inc. produces two coffee blends. Those are American (A) and British (B). Two of his resources are constrained as Columbia beans, of which he can get at most 300 pounds that means 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.

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