Name: Paper Homework 1.2 Linear Functions 9. The owner of an ice cream franchise

Question

Name: Paper Homework 1.2 Linear Functions 9. The owner of an ice cream franchise must pay the parent c ompany $1000 per month plus S% of the monthl supplies is 50% of the revenue. a) Find a model giving the owner's monthl y revenue. Operating cost of the franchise includes a fixed cost of per month for items such as utilities and labor. The cost of ice cream and y expenses as a function of revenue and interpret its slope. (0+05)p+ 2.000+1000) 05+30o b) Find a model giving the monthly profit as a function of revenue. (0.5-0-0S)P (2L000+1000) c) Interpret the slope of your profit model. d) Determine the mohthly revenue needed to break even.

Explanation / Answer

9) a) The required model giving the owner's monthly expenses as a function of revenue is :

E = (50%+5%)R+(2600+1000)

i.e., E = (55%)R+3600

i.e., E = (55/100)R+3600

i.e., E = 0.55R+3600

And, the slope of this model is = 0.55

b) The required model giving the monthly profit as a function of revenue is :

P = R-E

i.e., P = R - (0.55R+3600)

i.e., P = (1-0.55)R-3600

i.e., P = 0.45R-3600

c) the slope of the profit model is 0.45

d) For break even, C = R ,i.e., P = 0

i.e., 0.45R-3600 = 0

i.e., 0.45R = 3600

i.e., R = 3600/0.45

i.e., R = 8000

Therefore, $8000 monthly revenue is needed to break even.

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