Word Problem # 1:
1) You recently watched an episode of "Fear of Zombies," and have decided to better prepare your home for the impending outbreak. You own a 1400 sq foot home, on a half-acre lot (that is roughly square). The home is situated in Enchanted Lakes area of Kailua, Hawaii. You and your housemates have decided on the following three immediate improvements:
a) You want to build a wall that is eight feet high, made out of concrete. You estimate the wall needs to be somewhere between 12 and 18 inches thick, with steel reinforcements. You want the wall to encircle the property, except for an area near the driveway (you'll put a metal gate there).
b) You want to design a water tower that can supply you and your housemates with enough water to last two months (notice I did not tell you how many housemates you have). The tower must also be high enough for you to see for eight miles around your property (or up to the mountains, whichever is closer).
c) You want to build as food storage area, with enough space to store food for six months for all of your housemates. You have three options for food "kits" - (1) MREs, (2) Canned items, (3) Whatever you could get from a trip(s) to COSTCO.
2) You and your housemates have $87,500 dollars saved up, and don't have the ability to take out a loan or any other means for getting additional funds (i.e. - you only get $87,500).
3) Answer the following questions:
a) How much money will the concrete wall cost if it is 12 inches thick?
b) How much money will the concrete wall cost if it is 18 inches thick?
c) Develop a formula so you can determine the cost of the wall as a function of its width.
d) What is the minimum height the water tower must be?
e) How many gallons of water must the tank hold?
f) Develop a formula to determine how long the water will last as a function of the number of housemates (for all housemates water must last two months).
g) How much will the water tower cost?
h) How larger (dimensions width, length, height) must the food storage area be?
i) Develop a formula to determine how much food you need (for six months) as a function of the number of housemates. Hint - calories count.
j) How much will the food cost for all housemates for six months?
k) Do you have enough money for all three improvements? If not, how many housemates can your $87,500 support?
Word Problem # 2:
1) Your mom recently called you to talk about an idea she had for her own business. Your mom has always had a green thumb, she could grow anything. She wants to start an organic produce delivery business in her local community (she lives in Gearhart, OR). A local college professor, who teaches business courses, told her to expect an initial customer base of 10% of the local community, with growth of 3% per year. Your mom has asked you to help her determine how much money she will need to start her business. You happily agree and tell your mom you'll need some more information. She provides you with the following:
a) She plans to sell kale (several popular varieties), carrots, heirloom tomatoes, asparagus, spinach, and beets. She plans to plant an equal number of each of her crops (i.e. - for each tomato plant, she'll plant on beet plant, one carrot, etc). She has 25 acres of land to use.
b) A standard box of produce will be sufficient for a family of four for one week.
c) One delivery truck will be enough to cover 20 families per day. Delivery truck should be a small pickup with a shell over the bed to protect the produce. Your mom doesn't want to drive a giant truck.
d) The professor told her to expect gas prices to fluctuate (according to normal seasonal changes) between $2.59 and $3.85 during the next year.
e) The USDA will pilot use your mom's business to pilot a new program to certify small farmers for organic certification. The certification will cost nothing for the first three years. After that, it is expected to cost 2% of revenue per year to maintain certification.
f) Her soil is very fertile, but will she said she'll likely use locally procured organic fertilizer.
g) She plans to only use organic and/or environmentally safe (proven) pest control methods.
h) Her property is on city water and she pays the residential rate.
i) She wants to use a local bank (one in Gearhart) for her loan.
2) Answer the following questions:
a) What will your mom need to charge, in the first year, to break even?
b) Develop a formula to show what your mom's profits will be each year as a function of # of families (customers).
c) Develop a graph showing how many customers (use # families as units) she will have from year one to year 25.
d) If prices remain constant (no inflation, etc), what will your mom's profit be in year seven?
e) Will your mom's prices be competitive compared to other options (i.e. - COSTCO, other stores, businesses in area)?
f) How much will she need to take out for her loan?
g) Develop a graph showing the required # of delivery trucks your mom will need, from year one to year 25.
h) How many months can she grow crops each year?
i) Develop an equation to determine the number of seeds, of each of her plants, she will need based on the predicted number of families that will order produce boxes.
j) How many seeds will she need to feed 25% of the local community's families? How much will these seeds cost?