Problema Solution
Apocalypse God Inc. makes two apocalypse survival weapons: the Zombie Sword and the 12-Gauge Zombie Gun. The company has the equipment to produce at most 600 Zombie Swords or 525 12-Gauge Zombie Guns. It takes 30 hours of labor to produce a Zombie Sword and 40 hours of labor to produce a 12-Gauge Zombie Gun. The company has up to 24,000 labor hours available each month for zombie weapon production. If the profit gained on each Zombie Sword is $18 and on each 12-Gauge Zombie Gun is $24, find the number of each kind the firm should manufacture to gain the maximum profit each month. Let the Zombie Sword represent the independent variable
Answer provided by our tutors
Let
x = the number of Zombie Swords, x>=0
y = the number of 12-Gauge Zombie Guns, y>=0
The company has the equipment to produce at most 600 Zombie Swords or 525 12-Gauge Zombie Guns.
x <= 600
y <= 525
It takes 30 hours of labor to produce a Zombie Sword and 40 hours of labor to produce a 12-Gauge Zombie Gun. The company has up to 24,000 labor hours available each month for zombie weapon production:
30x + 40y <= 24000
The profit is determined by the objective function:
F(x , y) = 18x + 24y
Lets draw the graph of the system of inequalities:
x >= 0
y >= 0
x <= 600
y <= 525
30x + 40y <= 24000
Look at the graph and find the notice the corner points:
There are 4 corner points: (600, 0),(600,150),(100, 525),(0, 525):
We calculate F(x ,y) for each point to find the maximum value (the biggest value for F):
F(600, 0) = 18*600 + 24*0 = 104800
F(600, 150) = 18*600 + 24*150 = 14,400
F(100, 525) = 18*100 + 24*525 = 14,400
F(0, 525) = 18*0 + 24*525 = 13,125
The company will gain maximum profit if it produces: 600 Zombie Swords and 150 12-Gauge Zombie Guns OR 100 Zombie Swords and 525 12-Gauge Zombie Guns.