Question

The Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requires 3 hours to assemble and 1/2 hour to paint, and the economy model requires 2 hours to assemble and 1 hour to paint. The maximum number of assembly hours available is 24 per day, and the maximum number of painting hours available is 8 per day. If the profit on the deluxe model is $94 per unit and the profit on the economy model is $72 per unit, how many units of each model will maximize profit?

Answer 1

Profit = 94X + 72 Y, where X and Y are the numbers of Deluxe and Economy models produced, respectively

Assembly hours per day: 24
Paint hours per day: 8
x: 3 hrs assemble, 1/2 hr paint;
y: 2 hrs assemble, 1 hr paint;

Equations are -

3X₁ + 2X₂ = 24

0.5 Y₁ + Y₂ = 8

The maximum number of deluxe units per day is (x):
Assembly: 24 [hours] / 3 [hours/unit] = 8 [units]
Paint: 8 [hours] / (1/2) [hour/unit] = 16 [units]

Limited by your assembly time, you can only produce at most 8 deluxe units. What about the eco units (y):
Assembly: 24 [hours] / 2 [hours/unit] = 12 [units]
Paint: 8 [hours] / 1 [hour/unit] = 8 [units]

Therefore

4 Deluxe = 12 hrs assembly, and 2 hrs paint
6 Economy = 12 hrs assemblyy, and 6 hrs paint

Now you put this numbers into your profit equation:
P(x = 4, y = 6) = 94(4) + 72(6) = 808