Two competing corporations are submitting data to the US Military to create chemical hot packs. The Military has stipulated that each hot pack may cost no more than 85 cents and must result in at least a 20degrees Celsius rise in temperature when activated. Which of the following companies is the Military going to hire?
Company A - 1.5g of Y results in a 5degrees Celsius rise in temp. Cost of chemical: $184.04/kg
Company B - 1.0g of Z results in a 2.5degrees Celsius rise in temp. Cost of chemical: $97.13/kg
Co A.
How much is needed? That's
1.5g x (20/5) = 6.0 grams.
Cost of 6.0 g is
$184.04 x (6.0/1000) = about $1.10 each.
You figures Co B the same way.
Thank you DrBob, that helps a lot!
Well, it seems like we have a hot competition between Company A and Company B for the military's chemical hot pack project. Let's crunch some numbers and bring the heat!
For Company A, 1.5g of Y results in a 5 degrees Celsius rise in temperature. Now, let's calculate the cost per hot pack if we use Company A's chemical:
1 hot pack requires (1.5g / 1.5g) = 1
1 hot pack gives (5 degrees Celsius / 1.5g) = 3.33 degrees Celsius per gram
To get a 20 degrees Celsius rise, we would need (20 degrees Celsius / 3.33 degrees Celsius per gram) ≈ 6g of chemical.
The cost of Company A's chemical per hot pack would be (6g * $184.04/kg) = $1104.24. Whoa, that's hot on the budget!
Now, let's move on to Company B. According to their data, 1.0g of Z results in a 2.5 degrees Celsius rise in temperature. Let's calculate the cost per hot pack for Company B:
1 hot pack requires (1.0g / 1.0g) = 1
1 hot pack gives (2.5 degrees Celsius / 1.0g) = 2.5 degrees Celsius per gram.
To reach a 20 degrees Celsius rise, we would need (20 degrees Celsius / 2.5 degrees Celsius per gram) = 8g of chemical.
The cost of Company B's chemical per hot pack would be (8g * $97.13/kg) = $777.04. Hmm, that seems like a cooler deal!
Considering that the Military wants each hot pack to cost no more than 85 cents, it looks like they will have to hire Company B since their chemical's cost per hot pack is way below the budget.
So, congrats to Company B for winning this hot and budget-friendly competition! Looks like they really know how to heat things up without burning a hole in the Military's pocket.
To determine which company the Military will hire, we need to compare the cost and temperature rise provided by each company's chemical.
Let's calculate the cost and temperature rise for both companies:
For Company A:
1.5g of chemical Y results in a 5-degree Celsius rise in temperature.
Cost of chemical Y = $184.04/kg
For Company B:
1.0g of chemical Z results in a 2.5-degree Celsius rise in temperature.
Cost of chemical Z = $97.13/kg
Now, let's calculate the cost and temperature rise per gram for both companies:
For Company A:
Cost per gram of chemical Y = ($184.04/kg) / 1000g = $0.18404/g
Temperature rise per gram of chemical Y = 5 degrees Celsius / 1.5g = 3.333 degrees Celsius/g
For Company B:
Cost per gram of chemical Z = ($97.13/kg) / 1000g = $0.09713/g
Temperature rise per gram of chemical Z = 2.5 degrees Celsius / 1.0g = 2.5 degrees Celsius/g
Now, let's compare the cost and temperature rise per gram for both companies:
For Company A:
Cost per gram = $0.18404/g
Temperature rise per gram = 3.333 degrees Celsius/g
For Company B:
Cost per gram = $0.09713/g
Temperature rise per gram = 2.5 degrees Celsius/g
Based on the information provided, Company B offers a lower cost per gram ($0.09713/g) compared to Company A ($0.18404/g). However, Company A provides a higher temperature rise per gram (3.333 degrees Celsius/g) compared to Company B (2.5 degrees Celsius/g).
Since the Military has stipulated that each hot pack should cost no more than 85 cents and must result in at least a 20-degree Celsius rise in temperature, we need to calculate whether these requirements are met by either company.
For Company A:
Cost of 1 hot pack using chemical Y = (1.5g) * ($0.18404/g) = $0.27606
Temperature rise of 1 hot pack using chemical Y = (1.5g) * (3.333 degrees Celsius/g) = 5 degrees Celsius
For Company B:
Cost of 1 hot pack using chemical Z = (1.0g) * ($0.09713/g) = $0.09713
Temperature rise of 1 hot pack using chemical Z = (1.0g) * (2.5 degrees Celsius/g) = 2.5 degrees Celsius
Comparing the results to the Military's requirements:
- Company A's hot pack costs $0.27606 and results in a 5-degree Celsius rise in temperature.
- Company B's hot pack costs $0.09713 and results in a 2.5-degree Celsius rise in temperature.
Based on the results, both companies meet the Military's temperature rise requirement of at least 20 degrees Celsius. However, neither company meets the cost requirement of the hot pack being no more than 85 cents. Therefore, the Military may need to consider other options or negotiate further with the companies.
To determine which company the Military will hire, we need to compare the cost and temperature rise of the chemical provided by each company.
Let's start with Company A's chemical:
- 1.5g of Y results in a 5 degrees Celsius rise in temperature.
- The cost of the chemical is $184.04 per kg.
Now let's calculate the cost per gram for Company A's chemical:
- Divide the cost per kg by 1000 to convert it to cost per gram.
- Cost per gram = $184.04 / 1000 = $0.18404 per gram.
Next, let's calculate the cost of the chemical needed to achieve a 20 degrees Celsius rise in temperature for Company A:
- Based on the given information, we can set up a proportion:
(1.5g / 5 degrees Celsius) = (x grams / 20 degrees Celsius)
- Cross multiply and solve for x:
5x = 1.5g * 20 degrees Celsius
5x = 30g * degrees Celsius
x = 6g
So, Company A needs 6 grams of their chemical to achieve a 20 degrees Celsius rise in temperature.
Now let's calculate the cost of using Company A's chemical for a single hot pack:
- Cost of 6 grams = $0.18404 per gram * 6 grams = $1.10424
Since the cost of using Company A's chemical is $1.10424 per hot pack, which is higher than the allowed limit of 85 cents, Company A does not meet the cost requirement set by the Military.
Now let's move on to Company B's chemical:
- 1.0g of Z results in a 2.5 degrees Celsius rise in temperature.
- The cost of the chemical is $97.13 per kg.
Let's calculate the cost per gram for Company B's chemical:
- Divide the cost per kg by 1000 to convert it to cost per gram.
- Cost per gram = $97.13 / 1000 = $0.09713 per gram.
Next, let's calculate the cost of the chemical needed to achieve a 20 degrees Celsius rise in temperature for Company B:
- Based on the given information, we can set up a proportion:
(1.0g / 2.5 degrees Celsius) = (x grams / 20 degrees Celsius)
- Cross multiply and solve for x:
2.5x = 1.0g * 20 degrees Celsius
2.5x = 20g * degrees Celsius
x = 8g
So, Company B needs 8 grams of their chemical to achieve a 20 degrees Celsius rise in temperature.
Now let's calculate the cost of using Company B's chemical for a single hot pack:
- Cost of 8 grams = $0.09713 per gram * 8 grams = $0.77704
Since the cost of using Company B's chemical is $0.77704 per hot pack, which is lower than the allowed limit of 85 cents, Company B meets the cost requirement set by the Military.
Based on the cost and temperature rise criteria, the Military is likely to hire Company B since it meets both the cost limit of 85 cents and results in a 20 degree Celsius rise in temperature.