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 for maximize profit?

Answer 1

Profit maximizing equation is as follows:

Z = 12*X + 18*Y

Here,

X = Microeconomics and Y = Macroeconomics

It is subjected to constraints as follows:

12*X + 15*Y  $\leq$ 600 ---------- (1)

18*X + 9*Y $\leq$ 630 ------------- (2)

Equating both equations as mentioned above,

12*X + 15*Y = 600 ---------- (3)

18*X + 9*Y = ​​630 ------------- (4)

Multiplying equation 3 with 1.5 and subtracting equation 4 from it,

Y(15*1.5 - 9) = 900 - 630

Y = (900 - 630)/(15*1.5 - 9)

Y = 20

X = (600-15*20)/12

X = 25

So,

Maximized profit = 12*X + 18*Y = 12*25 + 18*20

Maximized profit = $660 and

Microeconomics to be produced = 25

Macroeconomics to be produced = 20