Example 3-1: Consider a family that drinks soda. Soda is a drink consisting of c

Question

Example 3-1: Consider a family that drinks soda. Soda is a drink consisting of carbonated water, flavoring and (usually) sweetener. The family's usual way of drinking it is buying 2-liter bottles of soda from a store at a price of $1.50 each. An alternative is to make soda on demand with a home soda machine. The machine carbonates a 1-liter bottle of water, and the user adds a small amount of separately purchased flavor syrup to produce a 1-liter bottle of flavored soda. An advantage of a home soda machine is that it can be easily stored, and use of flavor bottles removes the need to purchase and store soda bottles (which are mostly water) in advance. Soda machines cost $75 and come with several 1-liter empty bottles and a carbonation canister for 60 liters of water. Flavor syrup bottles cost $5 and make 50 8-ounce servings (12 liters) of flavored soda. Additional carbonation canisters cost $30. Question: If the family drinks 2 liters of soda per week (52 per year), compare the costs of 2-liter soda bottles with the purchase of a soda maker and flavor bottles in the first year period Answer:The cost of soda from a store is $1.50 * 1- $1.50 per week, or $78 per year. Note that this cost excludes any cost of gasoline or time required for shopping. For the soda machine option, we need a soda machine ($75) and sufficient flavor syrup bottles to make 104 liters of soda (about 9 bottles or $45), and would use the entire first (free) carbonation canister and most of a second ($30). Thus the soda machine cost for the first year year is $75+$45+ $30 =$150. This cost also excludes any cost of water, gasoline, or time (as well as unused syrup or carbonation). Over a one-year period, the life cycle cost or total cost of ownership for a soda machine is almost double that of store-bought bottles. The soda machine provides additional benefit for those who dislike routine shopping or have a high value of their time, which we noted has not been included.

Explanation / Answer

Spends in different options

Option 1: Get soda bottles

Assumption : Person goes for shopping every week and buy a single bottle

let c be the cost per hour

spend = 1.5* 52 + 52*c*3/60 = 78+52*c/20

Option 2: make homemade soda

Assumption - It would be real easy if they could mention the life span of the machine. But let's assume 1yr here

spend = $75+$45+$30 = $150

to equal the spends

78+c/20 *52 = 150

c= 72*20/52

c = $27.70 per hour

Part 2

spend1 = 1.5* 52 + 52*20*t/60 = 78+52t/3

Here t is the minutes spent in shopping

Spend 2 = 150

78+52t/3 = 150

t = 72*3/52 = 4.15 min

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