Question

3. The Branline Corp. produces treated fence posts in an old plant with these production and price data:

Q = 10X + 4Y + 0.2XY

Where Q = number of treated of fence post produced per day

X = machine hours of cutting and shaping machinery used per day

Y = labor hours used per day

Px = RM250 per unit

Py = RM100 per unit

When the daily operating budget is RM1500, determine the maximum number of treated fence posts that can be produced per day. Also, specify the optimal number of labor hours and machine hours used each day.

Answer 1

Q = 10X + 4Y + 0.2XY, and 1500 = 250*X + 100*Y, then MCx = 10 + 0.2Y, MCY = 4 + 0.2X.
1) MCx/ MCY = PX/PY, (10+0.2Y)/(4+0.2X) = 2.5, then 10+0.2Y = 10+0.5X, Y=2.5X
2) 1500 = 250X + 250X, where Y = 2.5X, X = 3, Y = 7.5, Q = 64.5.