Question

Product Manufacture Now that the design has been proven to be safe, Mr. Momo starts to think about the manufacturing process of the wing. There are three types of wings to be manufactured for different aircraft types, namely Wing A, Wing Band Wing C. Apart from the aluminum, three other materials to be used are titanium, fibre glass and duralumin. The total amount of titanium, fibre glass and duralumin bought each month by Momo Air are 1.92 kilotonne, 1.02 kilotonne and 1.22 kilotonne, respectively. Mr. Momo's team gives you the following information regarding the manufacture of each wing: One Wing A requires 8 tonne of titanium, 2 tonne of fibre glass and 4 tonne of duralumin One Wing B requires 6 tonne of titanium, 6 tonne of fibre glass and 2 tonne of duralumin One Wing Crequires 4 tonne of titanium, 2 tonne of fibre glass and 6 tonne of duralumin 5. Solve for the number of Wings A, B and C that Momo Air can manufacture each month using a suitable numerical method. If Momo Air decides to change the monthly total amount of materials to 2.6 kilotonne of titanium, 1.8 kilotonne of fibre glass and 2.0 kilotonne of duralumin, determine the number of Wings A, B and C that can be manufactured each month? Hint: use relaxation =1 for Gauss Seidel method

Answer 1

s. Wling - A requres 8 tonne of titanium 2 tonne of fibre glass 4 tonne of duralumin Wing-B requires 6 tonne of titanium 6 tonne of fibre glass 2 tonne of duraluna Wing-c requires & tonne of titanium 2 tonne of fibre glass 6 tonne of dwalumin = 1800 tonne Total titanium 2.6 kilotonne = 2600 tonne Total fibre glass = 1.8 kilotonne Total duralumin = 2.0 kilotonne > 2000 tonne Titanium 8A +63 +4-0 - 2600 fibie glass 2A + 6 B + 20 Durelimin: 4A + 2B + 6c 2000 Writing equation 0.6, o in matrix form 8 2600 = 1800 6 A 2 6 2 B 1800 4 2 < C 12000

auss- elimination method Augurmented from 5 6 4 2600 (AC) - 6 2 1800 4 2 6 2OOD - AR-Ri R₃- 2R₃ - Ri 8 6 260o N o 18 + 4600 O 8 1400 9R₂ + R₂ 8 6 4 2600 4 4600 10 76.17,200) SA +63 +40 2600 18 B +4C = 4600 762 = 17,200 fron from 6 160 =17,200 18 B +44 24600 1813 +4+22.336-4600 from ② 8A +63+46 = 2600 c=226.316 SA+61205 26 +4x22636 = 2644 226 B-205.26 205 A =5789 Y58 s8 wings of a 205 wings of a wings 2.26 can be manufactured