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 6500 televisions/month, whereas the output at Location II is at most 5300 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 3000 and 3600 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 $6 $4    Location II $8 $7    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 =       subject to the constraints Location I production             Location II production             Location II to City A shipping             Location II to City B shipping             Location I to City A shipping       x ≥ 0 Location I to City B shipping       y ≥ 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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 6500 televisions/month, whereas the output at Location II is at most 5300 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 3000 and 3600 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 $6 $4   
Location II $8 $7   


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 =
 
 
 
subject to the constraints
Location I production      
 
 
 
Location II production      
 
 
 
Location II to City A shipping      
 
 
 
Location II to City B shipping      
 
 
 
Location I to City A shipping       x ≥ 0
Location I to City B shipping       y ≥ 0
Expert Solution
Step 1

Given that TMA manufactures 37-inch high-definition LCD televisions in two separate locations: Location I and Location II. The output of location I is at most 6500 televisions per month and output of location II is at most 5300 per month.

It is given that TMA is main supplier of televisions to Pulsar Corporation.

In a certain month, Pulsar placed orders for 3000 and 3600 televisions to be shipped to two of its factories located in City A and City B, respectively. The shipping cost (in dollars) per televisions  from the two TMA plants to the two Pulsar factories are as follows:

From TMA/ To Pulsar factories City A City B
Location I $6 $4
Location II $8 $7
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