The WeedWacker Company
Quitta123 via MathKB.com
model and a gas model. The company has contracted to supply a national
discount retail chain with a total of 30,000 electric trimmers and 15,000 gas
trimmers. However, Weedwacker's production capablility is limited in three
departments: production, assemb;y, and packaging. The following table
summarizes the hours of processing time available an dthe processing time
required by each department, for both types of trimmers:
Hours Required per Trimmer
electric gas hours available
Production 0.20 0.40 10,000
Assembly 0.30 0.50 15,000
Packaging 0.10 0.10 5,000
The company makes its electric trimmer in house for $55 and its gas trimmer
for $85. Alternatively, it can buy electric and gas trimmers from another
source for $67 and $95, respectively. How many gas and electric trimmers
should Weedwacker make and how many should it buy from its competitor to
fulfill its contract in the least costly manner?
A. formulate an LP model for this problem.
B. What is the optimal solution?
--
Message posted via http://www.mathkb.com
Paul Sperry
wrote:
What have _you_ done so far?
--
Paul Sperry
Columbia, SC (USA)
Quitta123 via MathKB.com
>> The Weedwacker company manufactures two types of lawn trimmers: an electric
>> model and a gas model. The company has contracted to supply a national
>> A. formulate an LP model for this problem.
>> B. What is the optimal solution?
>
>What have _you_ done so far?
>
constraints are 20x1 +40x2<= 10000
30x1 +50x2<=15000
10x1 +10x2<=5000
x1>=0,x2>=0
--
Message posted via MathKB.com
http://www.mathkb.com/Uwe/Forums.aspx/algebra-help/200809/1
Paul Sperry
wrote:
> Paul Sperry wrote:
> >> The Weedwacker company manufactures two types of lawn trimmers: an electric
> >> model and a gas model. The company has contracted to supply a national
> >[quoted text clipped - 17 lines]
And here they are:
>>>discount retail chain with a total of 30,000 electric trimmers and
>>>15,000 gas trimmers. However, Weedwacker's production capablility is
>>>limited in three departments: production, assemb;y, and packaging.
>>>The following table summarizes the hours of processing time
>>>available an dthe processing time required by each department, for
>>>both types of trimmers:
>>>
>>>Hours Required per Trimmer
>>> electric gas hours
available
>>>Production 0.20 0.40 10,000
>>>Assembly 0.30 0.50 15,000
>>>Packaging 0.10 0.10 5,000
>>>
>>>The company makes its electric trimmer in house for $55 and its gas
>>>trimmer for $85. Alternatively, it can buy electric and gas trimmers
>>>from another source for $67 and $95, respectively. How many gas and
>>>electric trimmers should Weedwacker make and how many should it buy
>>>from its competitor to fulfill its contract in the least costly
>>>manner?
> >> A. formulate an LP model for this problem.
> >> B. What is the optimal solution?
> >
> >What have _you_ done so far?
> >
> I came up with the MAX: 30000x1 + 15000x2
> constraints are 20x1 +40x2<= 10000
> 30x1 +50x2<=15000
> 10x1 +10x2<=5000
> x1>=0,x2>=0
Well, the constraints are close. To clean up the notation a little, let
x be the number of electric units manufactured in house and y the
number of gas units manufactured in house.
Looking at the times we have
0.2*x + 0.4*y <= 10,000 or, handier, 2x + 4y <= 100,000.
Similarly 3x + 5y <= 150,000 and x + y <= 50,000.
The default constraints x >= 0 and y >= 0 are usually just assumed.
Now note you want the "least costly manner" so you want to _minimize_
the cost. Your objective function is the cost function.
I'll get you started.
For the electric units, the in house cost is $55/unit or 55x total. But
they must supply 30,000 units. If x is less than 30,000 they must go
outside and buy units at $67 per unit for 30,000 - x units so the total
cost of the outside units is 67(30000 - x). Notice this gives an
additional constraint : x <= 30,000.
Now finish it up.