Problema Solution
Scott owns a manufacturing company that produces two models of entertainment centers. The Athens requires 4 feet of fancy molding and takes 4 hours to manufacture. The Barcelona needs 15 feet of molding and 3 hours to manufacture. In a given week, there are 120 hours of labor available and the company has 360 feet of molding to use for the entertainment centers. The company makes a profit of $9 on the Athens and $12 on the Barcelona. How many of each model should the company manufacture to maximize its profit?
Answer provided by our tutors
let
a = the number of models of Athens manufactured, a>=0
b = the number of models of Barcelona manufactured, b>=0
in a given week, there are 120 hours of labor available and the company means:
4a + 3b <= 120
the company has 360 feet of molding to use for the entertainment centers:
4a + 15b <= 360
The objective function (the profit) is: F(a, b) = 9a + 12b
The constrains are:
4a + 3b <= 120
4a + 15b <= 360
a>=0
b>=0
graph the inequalities to find the feasible region and the vertices
click here to see the graph:
The vertices are (15, 20), (30, 0) and (0, 40).
We can find the maximum value by testing F(a,b) at each of the vertices.
At the four vertices of this region, the objective function has the following values:
F(15, 30) = 9*15 + 30*12 = $495
F(30, 0) = 9*30 + 30*0 = $270
F(0, 40) = 0*30 + 40*12 = $480
Thus, the maximum value of F(x,y) is $495, and this occurs when 15 models of Athens and 30 models of Barcelona are manufactured.