Financial Algebra Basic Question and Answer

- Rich and Betsy Cuik started a small business. They manufacture a microwavable coffee-to-go cup called Cuik Cuppa Coffee. It contains spring water and ground coffee beans in a tea-bag-like pouch. Each cup costs the company $1.00 to manufacture. The fixed costs for this product line are $1,500. Rich and Betsy have determined the demand function to be q = –1,000p + 8,500, where p is the price for each cup.
- Write the expense equation in terms of the demand, q.
- Express the expense equation found in part a in terms of the price, p.
- Determine a viewing window on a graphing calculator for the expense function. Justify your answer.
- Drawandlabelthegraphoftheexpensefunction.
- Write the revenue function in terms of the price.
- Graph the revenue function in a suitable viewing window. Whatprice will yield the maximum revenue? What is the revenue atthat price? Round both answers to the nearest cent.
- Graph the revenue and expense functions on the same coordinate plane. Identify the points of intersection using a graphing calculator. Round your answers to the nearest cent. Identify the price at the breakeven points.

2.Orange-U-Happy is an orange-scented cleaning product that is manufactured with disposable cloth pads. Each box of 100 pads costs $5 to manufacture. The fixed costs for Orange-U-Happy are $40,000. The research development group of the company has determined the demand function to be q = –500p + 20,000, where p is the price for each box.

- Write the expense equation in terms of the demand, q.
- Express the expense function in terms of the price,p.
- Determine a viewing window on a graphing calculator for theexpense function. Justify your answer.
- Draw and label the graph of the expense function.
- Write the revenue function in terms of the price.
- Graph the revenue function in a suitable viewing window. Whatprice will yield the maximum revenue? What is the revenue atthat price? Round answers to the nearest cent.
- Graph the revenue and expense functions on the same coordinate plane. Identify the points of intersection using a graphing calculator, and name the breakeven points. Round to the nearest cent. Identify the price at the breakeven points.

3.A supplier of school kits has determined that the combined fixed and variable expenses to market and sell G kits is W.

- What expression models the price of a school kit at the breakeven point?
- Suppose a new marketing manager joined the company and determined that the combined fixed and variable expenses would only be 80% of the cost if the supplier sold twice as many kits. Write an expression for the price of a kit at the breakeven point using the new marketing manager’s business model.

4.SeaShade produces beach umbrellas. The expense function is E = –19,000p + 6,300,000 and the revenue function is

R = –1,000p2 + 155,000p.

- Graph the expense and revenue functions. Label the maximumand minimum values for each axis. Circle the breakeven points.
- Determine the prices at the breakeven points.
- Determine the revenue and expense amounts for each of thebreakeven points.

5.Greengard’s manufactures and sells yard furniture made out of recycled materials. It is considering making a lawn chair from recycled aluminum and fabric products. The expense and revenue functions are E = –1,850p + 800,000 and R = –100p2 + 20,000p.

- Determine the profit function.
- Determine the price, to the nearest cent, that yields the maxi-mum profit.
- Determine the maximum profit, to the nearest cent.

6.An electronics store is selling car chargers for cell phones. The expense function is E = –300p + 13,000 and the revenue function is R = –32p^2+ 1,200p.

- At what price would the maximum revenue be reached?
- What would that maximum revenue be? Round to the nearestcent.
- Graph the expense and revenue functions. Circle the breakevenpoints.
- Determine the prices at the breakeven points. Round to the near-est cent.
- Determine the revenue and expense amount for each of the

breakeven points. Round to the nearest cent.

**Ans.** 6(1)

6(2)

**Ans** 6(3)

The straight black line is the expense function and the purple curve is the revenue function.

**Ans**.6(4)

**Ans **6(5)

**Question 7**.(a)At what price is the maximum profit reached in given graph

7(b) What are the breakeven prices?

7(c) Name two prices where the revenue is greater than the expenses.

7(d)Name two prices where the revenue is less than the expenses.

**Ans** 7(a)

**Ans** 7(b)

**Ans** 7(c)

**Ans** 7(d)

**Question 8.**

Examine each of the graphs in Exercises 2–5. In each case, the blue graph represents the expense function and the black graph represents the revenue function. Describe the profit situation in terms of the expense and revenue functions.

**Ans**:8(2)

**Ans:**8(3)

Clearly, area under parabolic curve is more hence there is net profit

**Ans**:8(4)

From the graph area under blue line is much more than area under parabolic line hence there is loss.

**Ans:**8(5)

area under blue curve is much less than area under parabolic curve hence there is profit.

**Question 9:**

write the profit function for the given expense and revenue functions.

When E = –20,000p + 90,000 & R = –2,170p^2 + 87,000p

**Ans:**

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