Question 1198669
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Formulate but do not solve the following exercise as a linear programming problem.
TMA manufactures 37-in. high-definition LCD televisions in two separate locations: Location I and Location II. 
The output at Location I is at most 5,800 televisions/month, 
whereas the output at Location II is at most 5,100 televisions/month. 
TMA is the main supplier of televisions to Pulsar Corporation, its holding company, 
which has priority in having all its requirements met. 
In a certain month, Pulsar placed orders for 2,900 and 4,000 televisions to be shipped 
to two of its factories located in City A and City B, respectively. 
The shipping costs (in dollars) per television from the two TMA plants 
to the two Pulsar factories are as follows:
<pre>
                    To Pulsar Factories
                      City A  City B
From TMA Location  I    $5     $5
From TMA Location II    $8     $8
</pre>

TMA will ship x televisions from Location I to City A and y televisions from Location I to City B. 
Find a shipping schedule that meets the requirements of both companies while keeping costs, C (in dollars), 
to a minimum.

Minimize C=
Location II production:
Location II to City A shipping:
Location II to City B shipping:
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This post is very strange. &nbsp;It requests &nbsp;" formulate as a linear program problem ", 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;but in my view, &nbsp;this instruction is only to confuse a reader or to mock a reader.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I will show how to solve this problem in a simple way, practically &nbsp;MENTALLY, 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;without reducing to a linear program problem. &nbsp;&nbsp;It is good, &nbsp;let say, &nbsp;for a

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5-th grade student, &nbsp;if to teach him/her in a right way.


<pre>
Since the shipping cost per unit from Location  I to A and to B is the same $5,  and 

since the shipping cost per unit from Location II to A and to B is the same $8,



it MEANS that the most reasonable strategy is 

    (1)  to ship as many TVs as possible from Location I (5800)
         for cheaper shipping price to cities A and B,

    (2)  and then to ship the rest of TVs from Location II (2900 + 4000 - 5800 = 6900 - 5800 = 1100)
         for more expensive shipping price to cities A and B.



How these quantities 5800 from Location I  and 1100 from Location II will be distributed 
between the cities A and B, does not matter for the total shipping cost.


Such strategy provides the minimum total shipping cost.
</pre>

Solved.



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It is how one could solve this problem, &nbsp;based on common sense &nbsp;ONLY &nbsp;and without employing 

the &nbsp;Linear &nbsp;Programming method, &nbsp;so as not to make the public laugh and not to look like an idiot.


But it looks like the current &nbsp;Artificial &nbsp;Intelligence did not achieve  
such a level of thinking yet &nbsp;(based on common sense).



Actually, &nbsp;this problem, &nbsp;if to formulate it in a right way, &nbsp;without mentioning 
the &nbsp;Linear &nbsp;Programming method, &nbsp;would be a first class &nbsp;ENTERTAINMENT &nbsp;problem.



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<H3>For your info and for your better understanding:</H3>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;There is an entire class of entertainment problems, which I call  "quasi-Linear Programming method problems", 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;that are outwardly similar to Linear Programming, but are intended to be solved mentally.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Such problems are specially invented for those people who want to develop their mind and find a fun in it.



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Such problems are also very good for a hiring interview, &nbsp;if a company wants to find/(to employ) 
a specialist, &nbsp;who really knows the subject and is able to think independently on his or her own.


Such a test will distinct with &nbsp;100% &nbsp; precision a specialist from 
a balabol, who only is able to speak or to write very much, but can not think.