1. A small truck can load 12 boxes of A, 5 of B and 3 of C while a medium truck can load respectively 8, 10 and 5 units of A, B and C. A large truck can load 8, 12 and 10 boxes of A , B and C respectively. Using matrix algebra determine the number of small, medium and large trucks required to load a total of 104 boxes of A, 98 boxes of B and 67 boxes of C. (7)
Answers
A small truck can load 12 boxes of A, 5 of B and 3 of C while a medium truck can load respectively 8, 10 and 5 units of A, B and C. A large truck can load 8, 12 and 10 boxes of A , B and C respectively. Using matrix algebra determine the number of small, medium and large trucks required to load a total of 104 boxes of A, 98 boxes of B and 67 boxes of C.⏭️⏭️⏭️⏭️⏭️⏭️⏭️⏭️⏭️⏭️⏭️⏭️⏭️⏭️
Given : A small truck can load 12 boxes of A, 5 of B and 3 of C while a medium truck can load respectively 8, 10 and 5 units of A, B and C. A large truck can load 8, 12 and 10 boxes of A , B and C
To find : small, medium and large trucks required to load a total of 104 boxes of A, 98 boxes of B and 67 boxes of C
Solution:
S = 12A + 5B + 3C
M = 8A + 10B + 5C
L = 8A + 12B + 10C
A = 12S + 8M + 8L = 104 Eq1
B = 5S + 10M + 12L = 98 Eq2
C = 3S + 5M + 10L = 67 Eq3
3 * eq1 - 2 * eq2
=> 26S + 4M = 116
=> 13S + 2M = 58
5 * eq1 - 4*eq2
=> 48S + 20M = 252
=> 12S + 5M = 63
13S + 2M = 58 Eq4
12S + 5M = 63 Eq5
5 * eq4 - 2 * Eq2
41S = 164
S = 4
12(4) + 5M = 63
=> 5M = 15
=> M = 3
3S + 5M + 10L = 67
=> 12 + 15 + 10L = 67
=> 10L = 40
=> L = 4
4 Small Trucks
3 Medium trucks
3 Large Trucks
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