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Question 1139263: 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.
a. Write a model to describe the information presented.
The diagram above shows the solution set shaded purple. Matching it to the information given:
b. Determine how many of each model maximizes the profit?
c. What is the maximum possible profit?
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! 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
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