Answer:
300 cartons of food and 400 cartons of clothes
Step-by-step explanation:
Total weight = 16000lb
Total volume = 18000lb
Let number of food box be x
Let number of cloth box be y
therefore,
Maximize Z = 13x + 6y
Subject to :
20x + 30y ≤ 18000 (Divide through by 10)
40x + 10y ≤ 16000 (Divide through by 10)
2x + 3y ≤ 1800...............................(1)
4x + y ≤ 1600 ................................(2)
y ≤ 1600 - 4x
Substitute the value of y in equation (1)
2x +3(1600 - 4x) ≤ 1800
2x + 4800 - 12x ≤1800
-10x ≤ -3000
Divide all through by -10
x ≤ 300
Substitute x = 300 in equation (2)
y ≤ 1600 - 4(300)
y ≤ 1600 - 1200
y ≤ 400
Therefore, lines intersects at 300, 400 means we can 300 cartons of food and 400 cartons of clothes
Total people helped = 13x + 6y
= 13 (300) + 6(400)
= 3900 + 2400
= 6300
