Question 1194469: The Star Electronics Company produces two robotic vacuums.
The production process for each product is similar in that
both require a certain number of hours of electronic work
and a certain number of labour hours in the assembly
department. Robotic vacuum A takes 4 hours of electronic
work and 2 hours in the assembly shop. Robotic vacuum B
requires 3 hours in electronics and 1 hour in assembly.
During the current production period, 240 hours of
electronic time are available, and 100 hours of assembly
department time are available. Each robotic vacuum A sold
yields a profit of RM 700 while each robotic vacuum B
produced may be sold for a RM 500 profit.
Formulate a linear programming model for this problem.
a) Find the objective function
b) Identify the variable and list all the constraints
c) Calculate the intersection point.
d) Draw the graph with a complete label of the axis,
intersection point, line equation, and shaded region.
e) Find the optimal solution
Found 2 solutions by Edwin McCravy, mccravyedwin:
Answer by Edwin McCravy(20066)   (Show Source):
You can put this solution on YOUR website! The currency RM is the Malaysian ringgit, which is worth
about 23 cents in US currency.
Vacuums| A | B |
-------|----|----|limits
Number | x | y | ↓
-------|----|----|------
E. hrs.| 4x | 3y | 240 |
-------|----|----|-----|
A. hrs.| 2x | 1y | 100 |
-------|----|----|------
Profit |700x|500y|
Maximize P = 700x + 500y <--objective function
Subject to constraints:
4x + 3y ≤ 240
2x + y ≤ 100
x ≥ 0, y ≥ 0
We draw the graphs of the two lines,
Put = in place of ≤
Intercepts
4x + 3y = 240 (0,80), (60,0)
2x + y = 100 (0,100), (50,0)
Corner |
point | P = 700x + 500y
--------|----------------------------------------------
(0,0) | 700(0) + 500(0) = 0 + 0 = 0
(50,0) | 700(50) + 500(0) = 35000 + 0 = 35000
(30,40) | 700(30) + 500(40) = 21000 + 20000 = 41000 <--max. profit
(0,80) | 700(0) + 500(80) = 0 + 40000 = 40000
Optimum solution: Make 30 A's and 40 B's with a max profit of RM 41000
Edwin
Answer by mccravyedwin(409)  (Show Source):
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