3. Windies Bats produces two models of cricket bats,the Layle and the Gara. They
are produced on two separate assembly lines. Producing a Layle requires 2 hours
on Line I and 1 hour on Line II, while producing a Gara requires 1 hour on Line
I and 3 hours on Line II. Sixty hours available for production on Line I and
forty on Line II. The unit profit on the Layle is $150 while that on the Gara is
$200.

.....how many of each model maximizes the profit?

Let x = the number of Layles and y = the number of Garas.

Producing a Layle requires 2 hours on Line I....., while producing a Gara
requires 1 hour on Line I..... Sixty hours available for production on Line
I.....

  (the line I inequality)

Producing a Layle requires.....1 hour on Line II, while producing a Gara
requires....3 hours on Line II.  …..forty (hours available for production) on
Line II.

   (the line II inequality)

The unit profit on the Layle is $150 while that on the Gara is $200.



a. Write a model to describe the information presented.

Maximize 
subject to constraints


, 

The last two constraints tell us that the feasible region is
in the upper right hand part of the graph, QI

We draw the boundary line 2x+y=60, which has intercepts (30,0) and (0,60)

We draw the boundary line x+3y=40, which has intercepts (40,0) and (0,13 1/3)

We solve the system of the boundary lines by substitution or elimination
to find any points where they intersect which are vertices of the feasible region:


 
We get their point of intersection as (x,y) = (28,4)



We test the objective function at each of the four corner points:

(0,0)  P = 150x+200y = 150(0)+200(0) = 0+0 = 0
(30,0)  P = 150x+200y = 150(30)+200(0) = 4500+0 = 4500
(28,4)  P = 150x+200y = 150(28)+200(4) = 4200+890 = 5000
(0,0)  P = 150x+200y = 150(0)+200(4/30) = 0+8000/3 = 2666.67

So they should make 28 Layles and 4 Garas for a maximum profit of $5000

Edwin