Radford Castings can produce brake shoes on six different machines. The following table summarizes the manufacturing costs associated with producing the brake shoes on each machine along with the available capacity on each machine. If the company has received an order for 1,800 brake shoes, how should it schedule these machines?

Machine	Fixed Cost (in dollars)	Variable Cost (in dollars)	Capacity
1	1,000	21	450
2	950	23	550
3	875	25	700
4	850	24	350
5	800	20	550
6	700	26	850

(a)Formulate an ILP model for this problem to minimize the total cost (in dollars). (LetX_i= thenumber of brake shoes produced by machinei. LetY_i= 1ifX_i> 0and 0 otherwise. In your linking constraints, use the smallest possible value ofM_i.)

MIN:

Subject to:

total brake shoes produced--

b) Use a spreadsheet model for this problem and solve it. What is the optimal solution?

(X₁, X₂, X₃, X₄, X₅, X₆) =

Please use the values given in the problem.