Question

Question 1 (a) Callum's Castings is a small company producing high quality bronze figurines. The company's next project is to produce a range of up to three types of military figurines: the Hussar, the Fusilier and the Piper. To produce each figurine it has to go through three processes: casting, grinding and finishing. Each Hussar requires 400g of bronze, three hours for casting, 40 minutes for grinding and 40 minutes for finishing; each Fusilier requires 250g of bronze, two hours for casting, 30 minutes for grinding and 20 min- utes for finishing; each Piper requires 200g of bronze, two hours for casting, 20 minutes for grinding and 20 minutes for finishing. Bronze costs $10 per kilogramme, casting costs $5.50 per hour, grinding costs 20 cents per minute and finishing costs 25 cents per minute, and these are the only costs required in the production of the figurines. Every week there are 9 kg of bronze available, 120 hours available for casting, 16.5 hours available for grinding and 14 hours available for finishing. The company sells each Hussar for $50, each Fusilier for $35 and each Piper for $30. Given that the company can sell all of the figurines it produces, and that it wants to maximize its weekly profit from the production of figurines, find a linear programme that can be used to determine the number of each figurine produced per week, explaining clearly what each variable and each constraint represents. (4]

Answer 1

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Hewan rusilier Availability 9 X1000 400 250 120 Bronge your Casting this grinding mainly Premihangimin) 3 40 16-5X 60 14X60 let no Hussare sold Then, constraints bez 4, Fusilier be az A Piper be y 400% +250 xy + 200 % < 9000 -0 34+23+ 20 3120 - 6 69 69 4x4 + 3% + 2 <16.5X6-99-3) ang mga naging (19) — 44, +222 + 2y <14*6=84.-@ Portal bronze used as repsesented by ist constraint. Casting hours by second constraint Grinding hours by 3rd constraint Pinishing hours by 4th constraint. Now Cost to produce 44,%, ((x)= (-0.4.384 +0.25%+02 %)x10 + (334+ 2xy + 2x2)x 5.50 I dollar = 100 cents Bronze cost . Casting cost 20 cent/pes minte - 12.00 unit Chorus Act Byt 24 J4 12 + 144,1+ 2065 4 Bly J x 15. - 12 shown fo, Max fle) = 5024 + 35% +3073 - (). - 11:54 + 10:57,+83. 1500 cent /hour 15 3 hour