Question 1198669: 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:
To Pulsar Factories
From TMA City A City B
Location I $5 $5
Location II $8 $8
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:
Found 2 solutions by textot, ikleyn:
Answer by textot(100)   (Show Source):
You can put this solution on YOUR website! **Formulating the Linear Programming Problem**
**Variables:**
* Let 'x' be the number of televisions shipped from Location I to City A.
* Let 'y' be the number of televisions shipped from Location I to City B.
**Objective Function:**
* **Minimize Shipping Costs (C):**
* C = 5x + 5y + 8(2900 - x) + 8(4000 - y)
* C = 5x + 5y + 23200 - 8x + 32000 - 8y
* C = -3x - 3y + 55200
**Constraints:**
* **Location I Production Constraint:**
* x + y ≤ 5800
* **Location II Production Constraint:**
* (2900 - x) + (4000 - y) ≤ 5100
* 6900 - x - y ≤ 5100
* x + y ≥ 1800
* **Pulsar Factory A Demand:**
* x ≥ 0
* **Pulsar Factory B Demand:**
* y ≥ 0
**Therefore, the linear programming problem can be formulated as:**
**Minimize:**
C = -3x - 3y + 55200
**Subject to:**
* x + y ≤ 5800
* x + y ≥ 1800
* x ≥ 0
* y ≥ 0
**Note:**
* This formulation assumes that all production capacities at both locations can be used to fulfill Pulsar's orders.
* The shipping costs from both locations to City A and City B are the same, which simplifies the objective function.
This linear programming problem can then be solved using graphical methods, the simplex method, or other optimization techniques to determine the optimal shipping schedule (values of x and y) that minimizes the total shipping costs while meeting the production and demand constraints.
Answer by ikleyn(52814)  (Show Source):
You can put this solution on YOUR website! .
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:
To Pulsar Factories
City A City B
From TMA Location I $5 $5
From TMA Location II $8 $8
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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This post is very strange. It requests " formulate as a linear program problem ",
but in my view, this instruction is only to confuse a reader or to mock a reader.
I will show how to solve this problem in a simple way, practically MENTALLY,
without reducing to a linear program problem. It is good, let say, for a
5-th grade student, if to teach him/her in a right way.
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.
Solved.
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It is how one could solve this problem, based on common sense ONLY and without employing
the Linear Programming method, so as not to make the public laugh and not to look like an idiot.
But it looks like the current Artificial Intelligence did not achieve
such a level of thinking yet (based on common sense).
Actually, this problem, if to formulate it in a right way, without mentioning
the Linear Programming method, would be a first class ENTERTAINMENT problem.
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For your info and for your better understanding:
There is an entire class of entertainment problems, which I call "quasi-Linear Programming method problems",
that are outwardly similar to Linear Programming, but are intended to be solved mentally.
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, if a company wants to find/(to employ)
a specialist, who really knows the subject and is able to think independently on his or her own.
Such a test will distinct with 100% precision a specialist from
a balabol, who only is able to speak or to write very much, but can not think.
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