A laundry can purchase soap containing 30% water for a price of $0.30/kg FOB the soap manufacturing plant (i.e., at the soap plant before shipping costs, which are owed by the purchaser of the soap). It can also purchase a different grade of soap that contains only 5% water. The freight rate between the soap plant and the laundry is $6.05/100 kg. What is the maximum price the laundry should pay for the 5% soap?
basis - 100 kg soap mixture- solid soap - 70 kg water - 30 kg fob price of this soap = 100 *0.3 =30 dollars solid soap fob price = 30 *70/100 =21 dollars the fob price of water in this soap= 30-21 =9 dollars the freight rate of this soap = $ 6.05 /100 kg total cost of the soap = 30 + 6
To determine the maximum price the laundry should pay for the 5% soap, we need to consider the additional cost incurred due to the water content and the freight charges.
Let's calculate the cost of the 30% soap:
- Price of the soap at the manufacturing plant: $0.30/kg
- Water content in the soap: 30%
- Therefore, the actual soap content in the 30% soap is 100% - 30% = 70%
Now, we can calculate the cost of the actual soap per kilogram:
Cost per kg of soap = Price of soap at manufacturing plant / Actual soap content
= $0.30 / 0.70
= $0.4286 per kg
Next, let's factor in the freight charges:
Freight cost per kg = Freight rate / 100 kg
= $6.05 / 100 kg
= $0.0605 per kg
Now, we can calculate the total cost per kg of the 30% soap, including the water content and freight charges:
Total cost per kg of soap = Cost per kg of soap + Freight cost per kg
= $0.4286 + $0.0605
= $0.4891 per kg
Finally, let's calculate the maximum price the laundry should pay for the 5% soap:
- Water content in the 5% soap: 5%
- Actual soap content in the 5% soap: 100% - 5% = 95%
- The maximum price should be such that the total cost, including water and freight charges, is not more than the total cost of the 30% soap.
Maximum price per kg of 5% soap = Total cost per kg of 30% soap / Actual soap content in 5% soap
= $0.4891 / 0.95
= $0.514
Therefore, the maximum price the laundry should pay for the 5% soap is $0.514 per kg.
To determine the maximum price the laundry should pay for the 5% soap, we need to calculate the cost of the soap at the laundry, including the freight cost.
Step 1: Determine the cost of the soap at the manufacturing plant.
The price of the soap containing 30% water at the manufacturing plant is $0.30/kg.
Step 2: Calculate the cost of transporting the soap from the manufacturing plant to the laundry.
The freight rate between the soap plant and the laundry is $6.05/100 kg. Since the soap is sold in kilograms, we need to convert the freight rate to a price per kilogram.
Freight cost per kg = ($6.05 / 100 kg) = $0.0605/kg
Step 3: Determine the water content adjustment.
To compare the prices of the soaps with different water contents, we need to adjust the price of the soap with 30% water to reflect the difference in water content.
Let's calculate the price adjustment as follows:
Price adjustment = (30% - 5%) = 25%
Step 4: Calculate the adjusted price for the 30% soap.
Adjusted price = (Price at the plant) * (1 + Price adjustment)
Adjusted price = $0.30/kg * (1 + 25%) = $0.30/kg * 1.25 = $0.375/kg
Step 5: Calculate the maximum price for the 5% soap.
Maximum price for 5% soap = Adjusted price - Freight cost per kg
Maximum price for 5% soap = $0.375/kg - $0.0605/kg = $0.3145/kg
Therefore, the maximum price the laundry should pay for the 5% soap is $0.3145/kg.