Decora Accessories Manufactures a Variety of Bathroom Accessories,including Decorative Towel

Decora Accessories manufactures a variety of bathroom accessories,including decorative towel rods and shower curtain rods.Each of the accessories includes a rod made out of stainless steel.However,many different lengths are needed: 12",18",24",40",and 60".Decora purchases 60" rods from an outside supplier and then cuts the rods as needed for their products.Each 60" rod can be used to make a number of smaller rods.For example,a 60" rod could be used to make a 40" and an 18" rod (with 2" of waste),or 5 12" rods (with no waste).For the next production period,Decora needs 25 12" rods,52 18" rods,45 24" rods,30 40" rods,and 12 60" rods.What is the fewest number of 60" rods that can be purchased to meet their production needs? (a)Formulate an integer programming model in algebraic form for this problem.(b)Formulate and solve an integer programming model in a spreadsheet for this problem.