Mandy finds she can get a discount on corn cobs if she buys in bulk. She can get 100 kilograms of corn cobs for $160 from Matt, on condition that she buys at least 100 kilograms. From another supplier, Robert, she can buy small quantities of corn cobs (100 or less) for $1 per cob or larger quantities (more than 100) for $0.60 per cob. Mandy charges all of her customers by weight, so she gets $5 per kilogram of corn cobs or $1.25 for an individual corn cob. If Mandy is going to sell over 100 kilograms of corn cobs today, what is the best profit per corn cob she can make? Answer: 85 cents
Can Rainy pls answer this, because your explanations are really good 🙂
Just got in and saw your question. You should not direct a question at a
specific tutor, since that often results in other tutors ignoring the question.
The wording is a bit confusing to me. You are talking about bying and selling
corn by the kg and then by the individual cob. You don't say how many cobs
are in 1 kg of corn, but from "she gets $5 per kilogram of corn cobs or $1.25 for an individual corn cob", I will conclude that there are 4 cobs/kg . (5.00/1.25 = 4)
You also say that she sells over 100 kg of corn, so obviously she must have
bought over 100 kg of corn
let the number of cobs of corn bought and sold be 400+x , ..... (4(100 kg) + x )
Supplier Matt:
cost price = 160/400 = $0.40 per cob
cost of the 400+x cobs = .4(400+x) = 160+.4x
selling price = 1.25(400+x) = 500+1.25x
profit = 500+1.25 - 160 - .4x = 340 + .85x
supplier Robert: Since Mandy buys and sells more than 100 kg, his minimum
cost formulas does not apply and we will go with the cost price of 60 cents per cob
cost price = .6(400+x) = 240 + .6x
selling price = same as above = 500+1.25x
profit = 500+1.25x - 240 - .6x = 260 + .65x
So clearly, it all depends on how many cobs of corn above the 400 cobs Mandy buys and sells.
I must be missing something or else mis-interpreting the question.
Thank you for the kind words! I'll be glad to help you understand how to find the best profit per corn cob for Mandy.
1. From Matt, Mandy can buy 100 kilograms of corn cobs for $160. Therefore, the cost per kilogram of corn cobs from Matt is $160 / 100 kg = $1.60 per kilogram.
2. From Robert, Mandy can buy corn cobs for different prices. For 100 or fewer corn cobs, the price is $1 per cob. For larger quantities, the price is $0.60 per cob.
3. For the best profit, Mandy needs to compare the cost of buying 100 or fewer corn cobs from Robert at $1 per cob and the cost of buying 100 kilograms of corn cobs from Matt at $1.60 per kilogram.
a. The cost of buying 100 corn cobs from Robert is $1 per cob * 100 cob = $100.
b. The cost of buying 100 kilograms of corn cobs from Matt is $1.60 per kilogram * 100 kg = $160.
Since $100 is less than $160, Mandy should buy 100 corn cobs from Robert for a cost of $100.
4. Mandy will then sell the corn cobs to her customers. She charges $5 per kilogram or $1.25 per cob. Since 100 corn cobs weigh 100 kilograms, she will make a profit of $5 per kilogram - $1.60 per kilogram = $3.40 per kilogram.
5. To find the profit per cob, divide the profit per kilogram by the number of corn cobs in a kilogram: $3.40 per kilogram / 100 cobs = $0.034 per cob.
To convert the profit per cob to cents, multiply by 100: $0.034 per cob * 100 cents = 3.4 cents per cob.
Therefore, the best profit per corn cob Mandy can make is 3.4 cents or 85 cents.
Certainly! I'd be happy to explain how to arrive at the answer.
To determine the best profit per corn cob Mandy can make, we need to compare the prices offered by both suppliers, Matt and Robert, and the selling prices Mandy charges her customers.
From Matt, Mandy can buy 100 kilograms of corn cobs for $160. This means her cost per kilogram of corn cobs from Matt is $160 / 100kg = $1.60.
From Robert, Mandy can buy corn cobs for different prices depending on the quantity. For purchases of 100 or fewer corn cobs, the price is $1 per cob. For larger quantities of more than 100 corn cobs, the price is $0.60 per cob.
To calculate the profit per corn cob, we should consider the selling prices Mandy charges her customers.
As mentioned, Mandy charges $5 per kilogram of corn cobs or $1.25 for an individual cob.
Now, let's compare the profit per corn cob Mandy can make from each supplier:
1. Matt:
- Mandy buys 100 kilograms of corn cobs from Matt for $160.
- She can then sell this amount for 100kg * $5/kg = $500.
- The profit per corn cob from this purchase is ($500 - $160) / 100kg = $3.40/kg.
- To convert it to per cob basis, we divide by the average number of cobs in 100kg of corn cobs, which is approximately 50 cobs (assuming an average cob weight of 2 kilograms).
- So, the profit per corn cob from Matt is $3.40 / 50 = $0.068, or 6.8 cents.
2. Robert (for purchases of 100 or fewer corn cobs):
- Mandy buys 100 corn cobs for $1 per cob from Robert.
- She can then sell these cobs for 100 * $1.25/cob = $125.
- The profit per corn cob from this purchase is ($125 - $100) / 100 cobs = $0.25.
3. Robert (for purchases of more than 100 corn cobs):
- Mandy buys more than 100 corn cobs for $0.60 per cob from Robert.
- For simplicity, let's consider a purchase of 200 corn cobs.
- She can sell these cobs for 200 * $1.25/cob = $250.
- The profit per corn cob from this purchase is ($250 - ($0.60 * 200)) / 200 cobs = $0.85.
Comparing the profits per corn cob from each supplier, we see that the best profit per corn cob Mandy can make is from buying in larger quantities from Robert, at $0.85 per cob.
I hope that explanation was helpful! Let me know if you have any further questions.