A newly formed firm must decide on a plant location. There are two alternatives under consideration: locate near the major raw materials or locate near the major customers. Locating near the raw materials will result in lower fixed and variable costs than locating near the market, but the owners believe there would be a loss in sales volume because customers tend to favor local suppliers. Revenue per unit will be $189 in either case.OmahaKansas CityAnnual fixed costs ($ millions)$1.0 $1.2 Variable cost per unit$30 $45 Expected annual demand (units)9,925 10,225 Using the above information, determine which location would produce the greater profit. (Omit the “$” sign in your response.)Omaha would produce the greater gross profit of $
The correct Answer and Explanation is:
To determine which location would produce the greater profit for the firm, we need to calculate the total profit for each option (Omaha and Kansas City). The formula to calculate profit is:
[
\text{Profit} = (\text{Revenue per unit} – \text{Variable cost per unit}) \times \text{Expected demand} – \text{Fixed costs}
]
For Omaha:
- Revenue per unit = $189
- Variable cost per unit = $30
- Expected annual demand = 9,925 units
- Fixed costs = $1.0 million
Using the formula:
[
\text{Profit (Omaha)} = (189 – 30) \times 9,925 – 1,000,000
]
[
\text{Profit (Omaha)} = 159 \times 9,925 – 1,000,000
]
[
\text{Profit (Omaha)} = 1,577,175 – 1,000,000
]
[
\text{Profit (Omaha)} = 577,175
]
For Kansas City:
- Revenue per unit = $189
- Variable cost per unit = $45
- Expected annual demand = 10,225 units
- Fixed costs = $1.2 million
Using the formula:
[
\text{Profit (Kansas City)} = (189 – 45) \times 10,225 – 1,200,000
]
[
\text{Profit (Kansas City)} = 144 \times 10,225 – 1,200,000
]
[
\text{Profit (Kansas City)} = 1,472,400 – 1,200,000
]
[
\text{Profit (Kansas City)} = 272,400
]
Conclusion:
Omaha would produce a greater profit of $577,175 compared to Kansas City’s profit of $272,400.
Explanation:
The decision between the two locations depends on both fixed and variable costs. Omaha has lower fixed costs ($1.0 million) and lower variable costs per unit ($30), which is advantageous for reducing overall expenses. Despite Kansas City having a slightly higher expected demand (10,225 units vs. 9,925 units), its higher fixed costs ($1.2 million) and higher variable costs per unit ($45) significantly reduce its profit margin.
By calculating the profit for each location, Omaha clearly offers a greater gross profit, making it the better choice for plant location in terms of maximizing financial returns.