Problema Solution
cabinet X costs $50, requires 10 sq ft of floor space, and holds 30 cu ft of files. cabinet Y costs $60, requires 8 sq ft of floor space, and holds 24 cu ft. To get maximum storage, how many of each should be purchased with a budget limit of $600 and floor space of 100 sq ft?
Answer provided by our tutors
let
x = the number of Cabinets X, x>=0
y = the number of Cabinets Y, y>=0
we have budget limit of $600
50x + 60y <= 600 divide both sides by 10
5x + 6y <= 60
a floor space limit of 100 sq ft
10x + 8y <= 100 divide both sides by 2
5x + 4y <= 50
the storage F(x,y) = 30x + 24y
we need to find x and y so that the objective function F(x, y) has maximum
by drawing the system of inequalities
5x + 6y <= 60
5x + 4y <= 50
x>=0
y>=0
click here to see the graph
one of the three vertices (10,0) (0,10) (6,5) is where F(x, y) has maximum
for (10,0) we have F(10,0) = 30*10+24*0 = 300
for (0,10) we have F(0,10) = 30*0+24*10 = 240
for (6,5) we have F(6,5) = 30*6+24*5 = 300
There are two solutions:
10 Cabinets X should be purchased or
6 Cabinets X and 5 Cabinets Y should be purchased.