Question

URGENT!!!!

Please read the entire question then work out the problem. SHOW YOUR WORK. You will NOT receive credit if you do not show your work.

I am moving 82 weaned calves to wheat pasture. Calves average water requirement is 5 gallons per calf per day (5 gal/head/day). I need to purchase a new stock tank. I want to buy one that is big enough to handle 82 calves, but I also don't want to spend more money than I have to. I don't mind buying more than 1 tank if it is a better deal.
My options are:
Oval stock tank: 4' long x 2' wide x 2' tall $140
Oval stock tank: 6' long x 2' wide x 2' tall $210
Oval stock tank: 8' long x 3' wide x 2' tall $390
Round stock tank: 8' diameter x 2' tall $500

For purposes of this problem:
* 1 cubic foot of water is approximately 7.5 gallons.
* an oval tank is a rectangle with a semi-circle on 2 ends (draw it out)

What should I do??

Answer 1

Explanation:

First, let's calculate the total water required per day for all the calves:

82 calves x 5 gal/head/day = 410 gallons/day

Next, we can calculate the volume of water that each tank can hold:

4' x 2' x 2' oval tank: (4 x 2 x 2) + (π x 2² x 0.5) = 16 + 6.28 = 22.28 cubic feet = 166.5 gallons

6' x 2' x 2' oval tank: (6 x 2 x 2) + (π x 2² x 0.5) = 24 + 6.28 = 30.28 cubic feet = 227 gallons

8' x 3' x 2' oval tank: (8 x 3 x 2) + (π x 3² x 0.5) = 48 + 14.14 = 62.14 cubic feet = 466 gallons

8' diameter x 2' tall round tank: (π x 4² x 2) / 3 = 100.53 cubic feet = 754 gallons

To determine which tank(s) to purchase, we need to make sure that the total volume of water they can hold is at least 410 gallons.

Option 1 (4' x 2' x 2' oval tank) holds 166.5 gallons, so we would need to purchase at least 3 of them to meet the total water requirement (3 x 166.5 = 499.5 gallons). This would cost $420.

Option 2 (6' x 2' x 2' oval tank) holds 227 gallons, so we would need to purchase at least 2 of them to meet the total water requirement (2 x 227 = 454 gallons). This would cost $420.

Option 3 (8' x 3' x 2' oval tank) holds 466 gallons, so one tank would be enough to meet the total water requirement. This would cost $390.

Option 4 (8' diameter x 2' tall round tank) holds 754 gallons, which is more than enough to meet the total water requirement. However, it is the most expensive option at $500.

Based on these calculations, the best option would be the 8' x 3' x 2' oval tank, which can hold enough water for all the calves and is also the most cost-effective option.