Question

A small publishing company decides to use one section of its plant to produce two textbooks called Microeconomics and Macroeconomics. The profit made on each copy is $12 for Microeconomics and $18 Macroeconomics. Each copy of Microeconomics requires 12 minutes for printing and 18 minutes for binding. The corresponding figures for Macroeconomics are 15 and 9 minutes respectively. There are 10 hours available for printing and 10.5 hours available for binding. How many of each should be produced to maximize profit? Please briefly explain the steps to find the solution.

Answer 1

12x+15y=10*60( contraint 1)

x+1.25y=50

x=50-1.25y

18x+9y=10.5*60( constraint 2)

3x+1.5y=105

Putting constraint 1 into 2,

3(50-1.25y)+1.5y=105

150-3.75+1.5y=105

-2.25y=-45

y=45/2.25=20

x=50-1.25*20=25

Note: X is microeconomics and y is macroeconomics