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Starting a Business

Starting your own business can be exciting and daunting at the same time. Businesses use math when managing finances, determining production levels, designing products and packaging, and monitoring labor. A bakery can be a highly profitable and rewarding business. During this activity, you will apply the skills from Ch. 1 & 2 to navigate some of the issues facing bakery owners.

Application Practice

First, save this file to your hard drive by selecting Save As from the File menu. Then, answer the following questions. Click the white space below each question to maintain proper formatting.
Use Equation Editor when writing all mathematical expressions or equations.

1. You have recently found a location for your bakery and have begun implementing the first phases of your business plan. Your budget consists of $45,000 of your own savings, $3750 in gifts from your family, and a $100,000 small business loan (which must be repaid in full within 10 years).
a. What integer would represent your total budget? (show work)
$45,000+$3750+$100,000= $148750

b. The fees for renting business space and paying for utilities is estimated to cost 25% of the total budget calculated above. Let C stand for the cost of these fee. Write an algebraic expression that shows how to find C.

c. How much money is estimated for the cost of rent and utilities?

d. Imagine an investor has increased your total budget by $38,525. The investor does not need to be repaid. Rather, he becomes part owner of your business. Could you use the investor’s contributions to cover the estimated cost of the rent and utilities? Will this be enough money? As you answer this question, include an expression using an inequality symbol to support your answer.
Yes, it is enough money.

e. The expression below illustrates your remaining funds after paying for rent and utilities. How much money is left? Use words to explain how you arrived at your answer. What mathematical rule guides you through simplifying this expression?

The mathematical rule that guides me into simplifying this expression is P.E.M.D.A.S
I began by removing the dollar signs first and adding what was in the parenthesis which is the amount that we started off with. Add 100,000 from the small loan, plus the 45,000 from the savings and lastly the 3,750 in family gifts. This leaves us:
Next I multiplied 0.25*148,750 (this is the 25% of the rent and utilities) =37187.50
Add: 45,000+3,750+100,000=148,750
Add: 37,187.50+38,525= 75712.50
Then subtract: 148,750-75712.50= $73037.50

$45,000 + $3,750 + $100,000 - 0.25($100,000 + $45,000 + $3,750) + $38,525
2. You are trying to decide how to most efficiently use your oven. You do not want the oven running at a high temperature when you are not baking, but you also do not want to waste a lot of time waiting for the oven to reach the desired baking temperature.

The instruction manual on the industrial oven suggests the oven temperature will increase by 45 degrees Fahrenheit per minute. When the oven is initially turned on, the temperature is 70 degrees Fahrenheit.

a. Let x = the number of minutes that the oven has been on. Write an expression showing how the temperature will change.
b. Find the temperature of the oven after 9 minutes. Show work.

3. In your oven, you can fit three baking sheets with 10 scones each, two baking sheets with 20 cookies each, and one baking sheet with 2 scones and 12 cookies to bake them all at the same time.

a. Using the variable s to represent the cost of scones, and the variable c to represent the cost of cookies, write an expression that illustrates the total cost of all baked goods in the scenario above. Use all needed numbers from the explanation above (do not do any calculations or simplifying).

b. Simplify your expression from part a showing all steps.

c. Imagine you have decided to price the scones at $3.18 each and the cookies at $1.99 each. If you filled your oven three times as described above, how much total revenue would result from selling all the scones and cookies baked? Show work.
R=32(3.18) + 52(1.99)
R=101.76 + 103.48

d. Yesterday your store earned $801.36 just from the sale of scones. Write and solve an equation that represents how many were sold. Your equation should make use of at least one variable. If needed, round to the nearest whole number.

4. Your profit P is determined by subtracting the cost C, the amount of money it costs to operate a business, from the revenue R, the amount of money you earn from selling your product. Profit can be represented algebraically by the equations:

Profit = Revenue - Cost
P = R - C

a. Rewrite the formula to solve for C.

b. Imagine the cost of running the business for one day is $5,364 and your profit for that day is $2,818. What was the revenue for that day? Use words to explain the process that you used to arrive at this answer.
P=2,818 This is the profit
C=5,364 This is the cost
2,818=R-5,364 Profit = revenue – cost
R=2,818-5,364 Revenue=profit-cost

5. When managing a business, it is important to take inventory of where your money is spent. You have a monthly budget of $15,000. Refer to the table below and answer the questions that follow.
Show work for each question. Round your answers to the nearest tenth of a percent.

Category Cost Percentage
Labor $5,785
Materials 27.7%
Rent and utilities 25%
Miscellaneous $1,310
Total $15,000 100%

a. What percentage of the total monthly budget is spent on labor?

b. What percentage of the total monthly budget is spent on miscellaneous items?

c. How much do materials cost monthly?
27.7% x $15,000= Cost
0.277 x 15,000= 4155.
Materials cost $4,155 monthly

d. How much do rent and utilities cost monthly?
25% x $15,000= Cost
0.25 x 15,000= 3750.
Rent and utilities cost $3,750 monthly

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