Math algebra ice cream problem?

Question

Now, Scott wants to be competitive with his pricing, so he wants to use mathematical modeling to figure out his costs, revenues and profits.



4. Scott bought the ice cream stand building for $2,000.00 and he will spend an extra $200 on the plywood ice cream cone design from Part II.

The monthly rent for the space his building is on is $150.

a. Write a linear equation giving the total cost C of operating the ice cream stand for n months.

b. Assuming that Scott can bring in $350 per month, write the equation for the revenue R derived from n months of operation.

c. What is the formula for Scott’s profit from n months of operation?

d. At what point does Scott break even?

Answer 1

a.
Total Cost, C = 2000 + 200 + 150*n
or C = 2200 + 150n

b.
Revenue, R = 350n

c.
Profit = Revenue - Total Cost
P = 350n - (2200 + 150n)
P = 200n - 2200

d. Break even when
Revenue = Total Cost or Profit is zero
P = 200n - 2200
0 = 200n - 2200
n = 11 months

Answer 2

a. The total cost for n months is the building+ plywood + n months' rent @ $150
C(n) = 2000 + 200 + 150n
C(n) = 2200 + 150n

b. R(n) = 350n

c. Profit is the amount brought in - total cost
P(n) = R(n) - C(n)
OR
P(n) = 350n - 2200 + 150n
P(n) = 200n - 2200

d. Set P(n) = 0
0=200n-2200
n=11 months

Answer 3

2000 + 200 + 150N = 350N
initial + cone + monthly time N number months =
350 per month for N number of months

2200 + 150N = 350N ...now subtract 150N from both sides
2200 = 200N

an u get to solve it from hear - heere - ah rats - u know

all the best

Answer 4

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