Establishing a Product Line. National Metals Company (NMC) manufactures titanium shafts. Its equipment is capable of producing shafts in 10 lengths (in cm) as shown in the chart below, reflecting settings on its machinery. Setting up the machinery to produce one of these results costs $250. As a result, NMC has decided to make only a selected number of lengths. When a customer requests a given length, NMC may supply it from stock, if it happens to match one of the lengths in the production schedule. Otherwise, NMC trims a longer length to meet the order. The variable cost for producing the shafts is $20 per cm, and NMC receives revenue of $40 per cm. Trim waste can be sold to a recycler for $15 per cm. The demand requirements for the coming week are tabulated as follows; all demand must be satisfied.

LENGTH	32	34	36	38	40	42	44	46	48	50
DEMAND	12	4	7	8	16	7	12	5	8	3

A. WHAT IS THE OPTIMAL ASSORTMENT OF LENGTHS FOR NMC TO MANUFACTURE?

B. WHAT IS THE OPTIMAL PROFIT IN THE COMING WEEK?

THIS IS A LINEAR PROGRAMMING QUESTION. SO PLEASE EXPLAIN WITH OBJECTIVE FUNCTION, DECISION VARIABLES, CONSTRAINTS EQUATIONS AND ALSO WITH EXCEL SPREADSHEET