Problem $2(45$ pts$)$

You$$ve looking to create a business manufacturing tablets for children. You want to

manufacture low$-$end and high$-$end tablets, to ensure you reach a maximum of

customers. You expect the demand for types of tablets to be about the same: $900$ each

month. You have found two potential locations that could manufacture both types of

tablets for you: Syracuse, NY and Springfield, MA$.$ Each month, the plant in Syracuse

has the capacity to produce at most $800$ tablets, while the plant in Springfield could

produce up to $1,000$ tablets. At the Syracuse plant, one low$-$end tablet would require $2$

hours of skilled labor; a high$-$end tablet would also require $2$ hours of skilled labor. At the

Springfield plant, one low$-$end tablet would require $3$ hours of skilled labor, while a highend tablet would require $4$ hours of skilled labor. Each plant has a capacity of $4,000$

hours of skilled labor. You estimate you could make a profit of $$600$ for each low$-$end

tablet made in Syracuse, $$800$ for each high$-$end tablet made in Syracuse, $$1,000$ for

each low$-$end tablet made in Springfield, and $$1,300$ for each high$-$end tablet made in

Springfield.