NECO 2023 · Paper 2 · Q8

Linear programming & operations research

A company has three production facilities $P_1$ , $P_2$ and $P_3$ with capacities of 8, 10 and 19 units (in hundreds) per week. The units are shipped to four warehouses $A_1$ – $A_4$ requiring 6, 8, 8 and 15 units (in hundreds) per week. The transportation cost (in hundreds of naira) is given below.

	$A_1$	$A_2$	$A_3$	$A_4$	Capacity
$P_1$	19	30	50	10	8
$P_2$	70	30	40	60	10
$P_3$	40	8	70	20	19
Demand	6	8	8	15

Using the north-west corner rule:

(i)
obtain the initial basic transportation plan;
Show the answer
$P_1A_1 = 6$ , $P_1A_2 = 2$ , $P_2A_2 = 6$ , $P_2A_3 = 4$ , $P_3A_3 = 4$ , $P_3A_4 = 15$
(ii)
calculate the total cost of this plan.

Worked solution (try it first)

(i)

Start in the top-left cell and send as much as possible each time.
$P_1$ (8): 6 to $A_1$ , which is then full, and its last 2 to $A_2$ .
$P_2$ (10): 6 to $A_2$ , which is then full, and 4 to $A_3$ .
$P_3$ (19): 4 to $A_3$ , which is then full, and 15 to $A_4$ .

(ii)

Cost: $6(19) + 2(30) + 6(30) + 4(40) + 4(70) + 15(20)$ .
$= 114 + 60 + 180 + 160 + 280 + 300 = 1094$ (hundreds of naira).

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