Question 3

Analyse the following problem graphically:-

a.Maximize profit = $4 + $6y

Subject to x + 2y <= 8 hours

6x +4y<= 24 hours

What is the optimal solution? If the first constraint is altered to does the feasible region or optimal solution change? (12m)

b.From the above problem, the second constraint is 6x + 4y <= 24hours (time available on machine 2). If the firm decides that 36 hours of time can be made available on machine 2 (namely, an additional 12 hours) at an additional cost of $10, should it add the hours?(7m)