A computer manufacturing company wants to develop a monthly plan for shipping finished products from three of its manufacturing facilities to three regional warehouses. It is thinking about using a transportation LP formulation to exactly match capacities and requirements. Data on transportation costs $($in dollars per unit$),$ capacities, and requirements are given below. $($Let xij represent the flow from plant i to warehouse j$.)$

Warehouse $1$Warehouse $2$Warehouse $3$CapacitiesPlant $12\mathrm{.}421\mathrm{.}642\mathrm{.}103,750$Plant $23\mathrm{.}195\mathrm{.}631\mathrm{.}736,250$Plant $34\mathrm{.}113\mathrm{.}153\mathrm{.}102,750$Requirement$8,2501,7502,750$

$($a$)$

How many variables are involved in the LP formulation?

$($b$)$

How many constraints are there in this problem?

$($c$)$

What is the constraint corresponding to Plant $1?$

$($d$)$

What is the constraint corresponding to Warehouse $2?$