Problem $1$: $(25)$

Given: Massachusetts Block Company $($MBC$)$ has orders for $80$ tons of concrete masonry blocks at three

locations as follows:

Lowell $=25$ tons, Salem $=45$ tons, and Worchester $=10$ tons.

MBC has two plants; Plant $2$ can produce up to $50$ tons per week while Plant $1$ can only produce a

maximum of $40$ tons per week. The deliveries must be shipped through two warehouses before reaching

their final destination. Delivery costs per ton between each location and capacity at each location are

provided below:

Find:

a$)$ Formulate the LP problem with Network Diagram and mathematical expression for decision

variables, objective function, and constraints $(10)$

b$)$ Solve for the minimum cost shipping plan using Excel Solver. Illustrate the optimal shipping plan in

a network diagram. $(15)$