please! Problem $2-$ Network Design problem

Drylce Inc., is a manufacturer of air conditioners that has seen its demand grow significantly. The company

anticipates nationwide demand for the next year to be $180,000$ units in the South, $120,000$ units in the Midwest,

$110,000$ units in the East, and $100,000$ units in the West. Managers at Drylce are designing the manufacturing

network and have selected four potential sites$-$ New York, Atlanta, Chicago, and San Diego. Plants could have a

capacity of either $200,000$ or $400,000$ units. The annual fixed costs at the four locations are shown in Table

$1\mathrm{.}1$ and Table $1\mathrm{.}2,$ along with the cost of producing and shipping an air conditioner to each of the four markets.

Formulate the problem as a linear programming model to decide where Drylce should build its factories and their

capacities. You do Not need to solve it$.$

Production and transport costs for Drylce Inc.

Table $1\mathrm{.}1$ Demand Region

Table $1\mathrm{.}2$ Plant Option

a$.(6$ pts$)$ Clearly define decision variables

b$.(6$ pts$)$ What is the total cost $($define the objective function$)$ we are trying to minimize? First write the general

formulation and then substitute the numbers.

c$.(8$ pts$)$ What are the constraints? First write the general formulation and then substitute the numbers.

Supply constraint:

Demand constraint: