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Economics & Math: Equilibrium, Cost, Revenue, Profit, Break-Even, Papers of Mathematics

A collection of economics and mathematics problems aimed at finding market equilibrium points, cost and revenue functions, profit functions, and break-even quantities. The problems involve various equations and require the application of algebra and graphical analysis. Students and lifelong learners interested in economics, mathematics, or business may find this document useful for studying, summarizing, or practicing problem-solving skills.

Typology: Papers

Pre 2010

Uploaded on 08/18/2009

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10. Given supply is p = q + 350 and demand is p = 550 - 10q
a. Find the Market Equilibrium Point (q,p):_________________
Draw the first quadrant graph below or on separate paper
11. The variable cost of producing a palm pilot is $48 with fixed costs of $5890. The
phone sells for $110.
a. Find the Cost function_____________________________________
b. Find the Revenue function_____________________________________
c. Find the Profit function_______________________________________
d. Find the Break-Even quantity (x)__________________
12. An investor earns $370 on two bonds, one paying 9.5% and the other paying 12%.
If he has $3500 to invest, how much was invested in each bond?
8. You will invest $64000 in two types of rental units. You want to earn $10890 per year in
order to pay taxes and insurance. How much will you invest in each if one unit earns a 15%
return and the other one earns an 18% return?
9. Fixed costs per month for a small company is $1650 and the variable cost of their product is
$24. If each item sells for $57 each, find the following:
a. The Revenue Function: ___________________________
b. The Cost Function: _______________________________
c. The Profit Function: ______________________________
d. The Break-even quantity
10. The Supply function for a product is p = 6q + 125
The Demand function for that product is p = -2q +341
Find the Market Equilibrium point (q,p)
Lance Armstrong must consume 17000 calories each day during the Tour de France. If
the calories are split requiring 11900 calories from carbs and 5100 calories from protein,
how many ounces of the following foods should he eat per day. One ounce of spaghetti
with meat sauce gives 250 calories of carbs and 50 calories in protein. Each ounce of a
chicken salad sandwich gives 100 calories of carbs and 100 calories of protein.
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10. Given supply is p = q + 350 and demand is p = 550 - 10q

a. Find the Market Equilibrium Point (q,p):_________________

Draw the first quadrant graph below or on separate paper

11. The variable cost of producing a palm pilot is $48 with fixed costs of $5890. The

phone sells for $110.

a. Find the Cost function_____________________________________

b. Find the Revenue function_____________________________________

c. Find the Profit function_______________________________________

d. Find the Break-Even quantity (x)__________________

12. An investor earns $370 on two bonds, one paying 9.5% and the other paying 12%.

If he has $3500 to invest, how much was invested in each bond?

  1. You will invest $64000 in two types of rental units. You want to earn $10890 per year in order to pay taxes and insurance. How much will you invest in each if one unit earns a 15% return and the other one earns an 18% return?
  2. Fixed costs per month for a small company is $1650 and the variable cost of their product is $24. If each item sells for $57 each, find the following: a. The Revenue Function: ___________________________ b. The Cost Function: _______________________________ c. The Profit Function: ______________________________ d. The Break-even quantity
  3. The Supply function for a product is p = 6q + 125 The Demand function for that product is p = -2q + Find the Market Equilibrium point (q,p)

Lance Armstrong must consume 17000 calories each day during the Tour de France. If

the calories are split requiring 11900 calories from carbs and 5100 calories from protein,

how many ounces of the following foods should he eat per day. One ounce of spaghetti

with meat sauce gives 250 calories of carbs and 50 calories in protein. Each ounce of a

chicken salad sandwich gives 100 calories of carbs and 100 calories of protein.

  1. You will invest $19000 in two types of stock, General Electric and Computech. You want to earn $2170 per year in order to take a nice cruise to Alaska. How much will you invest in each if Computech earns a 19% return and General Electric earns a 7% return?
  2. Fixed costs per month for an ice-cream shoppe is $1020 and the variable cost on each scoop of ice-cream is $1.25. If each scoop of ice-cream sells for $2.75 each, find the following: a. The Revenue Function: ___________________________ b. The Cost Function: _______________________________ c. The Profit Function: ______________________________ d. The Break-even quantity
  3. The Supply function for a product is p = 5q + 170 The Demand function for that product is p = -3q + Find the Market Equilibrium point (q,p)
  4. A person on a special diet must have 500 calories in protein and 1500 calories in carbs per day. If chicken salad gives 100 calories of protein and 200 calories of carbs per cup, and wheat pasta gives 400 calories in carbs and 100 calories in protein per cup, how many cups of each should the diet contain?
  5. You will invest $75000 in two types of stock. You will need to earn $9810 per year in order to pay the taxes and insurance on your beach-front property. How much will you invest in each if one stock earns a 15% return and the other one a 9% return?
  6. Fixed costs per week for a computer company is $3250 and the variable cost on the computer they supply is $500. If the computers sell for $1150 each, find the following: a. The Revenue Function b. The Cost Function c. The Profit Function d. The Break-even quantity
  7. Given 3x - 7y = 4 a. find the equation of the line parallel to the given equation and containing the point (2, 4) b. find the equation of the line perpendicular to the given equation and containing the same point (2, 4)
  8. A person on a special diet must have 950 calories in protein and 2900 calories in carbs per day. If pinto beans give 150 calories of protein and 300 calories of carbs per cup, and wheat pasta gives 400 calories in carbs and 100 calories in protein per cup, how many cups of each should the diet contain?