ach 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