Question

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 11. The output at Location I is at most 5500 televisions/month, whereas the output at Location I is at most 5200 televisions/month. THA 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 2800 and 4100 televisions to be shipped to two of its factories located in City A and City 8, 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 From TMA City A $7 Location Location 1I 4 $7 TMA will shipx 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 dolars), to a minimum. C- subject to the constraints Minimize Location I production Location II production Location II to City A shipping Location II to City 8 shipping Location I to City A shipping x 0 y z0 Location I to City B shipping Need Help? Read

Answer 1

Since the problem statement does not mention it, we will assume that the cost of production of the television is the same at both the locations - Location I and Location II

Thus, we have to only minimize the shipping costs.
The shipping costs are as under

From TAM	To Pulsar City A	To Pulsar City B
Location I	IA = $7	IB = $4
Location II	IIA = $8	IIB = $7

Location I production = P1
Location II production = P2
Location II to City A Shipping = p >=0
Location II to City B Shipping = q >=0

Location I to City A Shipping = x >= 0
Location I to City B Shipping = y >= 0

The constraints on production are
P1 = x + y <= 5500
P2 = p + q <= 5200

Demand at City A, DA = 2800
Demand at City B, DB = 4100

Thus, DA = x + p = 2800
and DB = y + q = 4100

Also, Total Production = Total Demand (Supply)
Thus, P1 + P2 = DA + DB
(x+y) + (p+q) = 4100 + 2800 = 6900

The priority of both the production facilities is to supply the Television sets to Pulsar factories.

Now to restate the problem for which we have to solve
Minimize total cost of Shipping C = x * IA + y * IB + p * IIA + q * IIB
Minimize C = 7x + 8y + 4p + 7q

The problem is thus formulated.