Question

Situation:

Golden Star Corp. wants to optimize the profit ¶:

maximize: ¶ = 4 QA + 3 QB

Subject to the following machine-time constraints:

QA + 2 QB £ 100                  2 QA +   QB £ 100

And the non-negativity constraints:

QA , QB ³ 0

Questions:

Solve the problem using both algebraic and graphic approach. Check that both solutions are the same. Set up the associated dual problem and solve algebraically.

Answer 1

Algebraically:

The problem is:

max 4QA+ 3QB S.t. QA+20 = 100, and 20A+ QB =100

Solving the two constraints to obtain the values of :

and C

100 100 QA 100 2Q8 2(100 2QB) + QB 100 QA Qa 3 3

Plugging these values into the objective function:

400 300 700 4QA+30B +33 233.3

Graphically:

Plotting the objective function along with the constraints:

100 -80 -60 -40 (33.333, 33.333) 80 100 60 40 0 20 20

where the red curve is the objective function, and the green and the blue curves are the constraints.