A manufacturing plant requires 3\text{ tonnes} of localized raw material to produce 1\text… — JAMB UTME

A manufacturing plant requires $3\text{ tonnes}$ of localized raw material to produce $1\text{ tonne}$ of finished product. The raw material deposit and the market are separated by a distance of $100\text{ km}$ . Transport costs are $\$2.00\text{ per tonne-km}$ for raw materials and $\$3.00\text{ per tonne-km}$ for finished goods. An alternative production site, Location L, offers a labor cost savings of $\$400.00$ per tonne of finished product, but increases the transportation distance of raw materials by $30\text{ km}$ and finished goods by $10\text{ km}$ compared to the least-cost transport point. Based on Alfred Weber's location theory, what is the net financial gain or loss per tonne of finished product if the plant relocates to Location L?

A net gain of $\$190.00$ , indicating that Location L lies within the critical isodapane and is economically optimal.Answer
B
A net gain of $\$310.00$ , indicating that Location L reduces overall production costs significantly.
C
A net gain of $\$110.00$ , indicating that higher freight charges heavily offset cheap labor advantages.
D
A net loss of $\$110.00$ , indicating that Location L lies outside the critical isodapane and should be rejected.

Answer

A net gain of

\$190.00

per tonne of finished product, placing Location L inside the critical isodapane.

According to Alfred Weber's Industrial Location Theory, the least-cost transport location for a weight-losing industry (

MI = 3 > 1

) is at the raw material origin, where moving input costs

\$6.00/\text{km}

versus

\$3.00/\text{km}

for output. Moving production to Location L adds

\$180.00

in raw material transport (

3\text{ tonnes} \times \$2.00 \times 30\text{ km}

) and

\$30.00

in finished goods transport (

1\text{ tonne} \times \$3.00 \times 10\text{ km}

), totaling

\$210.00

extra transport costs. Because the labor savings (

\$400.00

) exceeds the additional transport expense (

\$210.00

), Location L yields a net savings of

\$190.00

per tonne and lies inside the critical isodapane.

Step-by-Step Solution

Determine the least-cost transport location

Transport cost per km for raw material assembly =

3\text{ tonnes} \times \$2.00/\text{tonne-km} = \$6.00/\text{km}

. Transport cost per km for finished goods distribution =

1\text{ tonne} \times \$3.00/\text{tonne-km} = \$3.00/\text{km}

. Since assembly cost per km exceeds distribution cost per km, the least-cost transport location is at the raw material deposit.

Weber's theory dictates that when the Material Index is greater than 1 (

MI = 3/1 = 3

), manufacturing is weight-losing and least-cost transport points favor raw material sites.

Calculate additional transportation costs incurred by moving to Location L

Additional raw material transport cost =

3\text{ tonnes} \times \$2.00/\text{tonne-km} \times 30\text{ km} = \$180.00

. Additional finished goods transport cost =

1\text{ tonne} \times \$3.00/\text{tonne-km} \times 10\text{ km} = \$30.00

. Total additional transport cost = \

180.00 + \$30.00 = \$210.00

Deviating from the optimal transport location increases movement costs for both input and output.

Compute net financial impact incorporating cheap labor savings

Net financial advantage = Labor cost savings - Total additional transport cost = \

400.00 - \$210.00 = +\$190.00\text{ per tonne}

If labor savings exceed the additional transport costs, the factory relocates to the labor site (Location L lies within the critical isodapane).

Key Concept

Weber's Least Cost Theory: Critical Isodapane and Labor Deviation

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