per week. Each product requires the following processing times $($in hours$)$ on each

of three machines.

Product $1$ Product $2$ Product $3$

Machine $1221$

Machine $2346$

Machine $3465$

Each machine must be run by one of $19$ cross$-$trained workers who are each available

$35$ hours per week. The plant has $10$ type $1$ machines available, $6$ type $2$ machines

available, and $8$ type $3$ machines available. Products $1,2,$ and $3$ contribute $$90,$ $$120,$

and $$150,$ respectively, in marginal profit per unit produced.

a$.$ Formulate an LP model for this problem.

b$.$ Implement your model in a spreadsheet and solve it$.$

c$.$ What is the optimal solution?

d$.$ How many workers should be assigned to each type of machine?