Exam 5: Applications of Linear Equations

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5, select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart to solve the following problem: Clone Computers assembles and packages personal computer systems from brand-name components. Its Home Office PC System is assembled from components costing $1400 per system and sells for $2000. Labour costs for assembly are $100 per system. This product line's share of overhead costs is $10,000 per month. a) How many Home Office Systems must be sold each month to break even on this product line? b) What will be the profit or loss for a month in which 15 Home Office Systems are sold?

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5, select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart to solve the following problem: A small manufacturing operation can produce up to 250 units per week of a product that it sells for $20 per unit. The variable cost per unit is $12, and the fixed cost per week is $1200. a) How many units must it sell per week to break even? b) Determine the firm's weekly profit or loss if it sells: (i) 120 units per week (ii) 250 units per week c) At what level of sales will the net income be $400 per week?

The current annual budget for Armstrong Ltd. indicates total revenue of $8,000,000. The total variable costs are $1,600,000 and fixed costs are $5,600,000. Calculate break-even revenue per year.

Determine the slope and y-intercept of each of the following equations: -6x = 9y

Solve the following problem using the Contribution Margin Approach. Valley Peat Ltd. sells peat moss for $10 per bag. Variable costs are $7.50 per bag and annual fixed costs are $100,000. a) How many bags of peat must be sold to break even? b) What will be the net income for a year in which 60,000 bags of peat are sold? c) How many bags must be sold for a net income of $60,000 in a year? d) What annual sales in terms of bags and in terms of dollars would produce a loss of $10,000? e) How much do the break-even unit sales and break-even revenue increase per $1000 increase in annual fixed costs?

The formula for converting from Celsius temperatures, C, to Fahrenheit temperatures, F, is F = C + 32. a) If you were to plot a graph of F vs. C, what would be the slope and F-intercept of the line? b) The slope represents the change in F per unit change in C. Use the value of the slope to determine the increase in Fahrenheit temperature corresponding to a 10 Celsius-degree rise. c) Rearrange the given formula to obtain a formula for converting from Fahrenheit temperatures to Celsius temperatures. What would be the slope and C-intercept if C vs. F were plotted on a graph?

Solve the following problem using the Contribution Margin Approach. CD Solutions Ltd. manufactures and replicates CDs for software and music recording companies. CD Solutions sells each disc for $2.50. The variable costs per disc are $1.00. a) To just break even, how many CDs must be sold per month if the fixed costs are $60,000 per month? b) What must sales be in order to have a profit of $7500 per month?

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5, select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart to solve the following problem: ChildCare Industries manufactures infant car seats that it sells to retailers for $155 each. The costs to manufacture each additional seat are $65, and the monthly fixed costs are $18,000. a) How many seats must be sold per year to break even? b) What will ChildCare's loss be if it sells 2000 seats in a year?

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5, select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart to solve the following problem: Bentley Plastics Ltd. has annual fixed costs of $450,000 and variable costs of $15 per unit. The selling price per unit is $25. a) What annual revenue is required to break even? b) What annual unit sales are required to break even? c) What will be the annual net income at annual sales of: (i) 50,000 units? (ii) $1,000,000? d) What minimum annual unit sales are required to limit the annual loss to $20,000? e) If the unit selling price and fixed costs remain the same, what are the changes in break-even unit sales and break-even revenue for a $1 increase in variable costs?

Solve the following problem using the Contribution Margin Approach. Huntsville Office Supplies (HOS) is evaluating the profitability of leasing a photocopier for its customers to use on a self-serve basis at 10′ per copy. The copier may be leased for $300 per month plus 1.5′ per copy on a full-service contract. HOS can purchase paper at $5 per 500-sheet ream. Toner costs $100 per bottle, which in normal use will last for 5000 pages. HOS is allowing for additional costs (including electricity) of 0.5′ per copy. a) How many copies per month must be sold in order to break even? b) What will be the increase in monthly profit for each 1000 copies sold above the break-even point?

Solve the following problem using the Contribution Margin Approach. In the year just ended, a small appliance manufacturer sold its griddle at the wholesale price of $37.50. The unit variable costs were $13.25, and the monthly fixed costs were $5600. a) If unit variable costs are expected to rise to $15.00 and fixed costs to $6000 per month for the next year, at what amount should the griddle be priced in order to have the same break-even volume as last year? b) What should be the griddle's price in order to have the same profit as last year on sales of 300 griddles per month in both years?

the graphical method to solve the following pair of equations.

Solve the following problem using the Contribution Margin Approach. Reliable Plastics makes containers that it sells for $2.55 each. Its fixed costs for this product are $2000 per month and the variable cost per unit is $1.30. a) What is the break-even point in units? b) What is the break-even sales revenue?

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5, select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart to solve the following problem: Ingrid processes and bottles jam in her home-based business. Her fixed costs are $250 per month and the variable cost per jar is $1.20. She sells the jam to local grocery stores for $3.20 each. a) How many jars must she sell per year to break even? b) What will be her profit if she sells 3000 jars in a year?

Solve the following set of equations graphically:

Solve the following problem using the Contribution Margin Approach. Genifax reported the following information for September: a) Determine the unit sales required to break even. b) What unit sales would generate a net income of $30,000? c) What unit sales would generate a profit of 20% of the sales dollars? d) What sales dollars are required to produce a profit of $20,000? e) If unit variable costs are reduced by 10% with no change in the fixed costs, what will the break-even point become?

A plumber charges a flat $50 for a home service call plus $10 per 15 minutes of labour. Write an equation for calculating the total charges, C, in terms of the hours of labour, H. If you were to plot a graph of C vs. H, what would be the slope and C-intercept of the line?

Solve the following problem using the Contribution Margin Approach. A college ski club is planning a weekend package for its members. The members will each be charged $270. For a group of 15 or more, the club can purchase a 2-day downhill pass and 2 nights' accommodation for $220 per person. A 36-passenger capacity bus can be chartered for $1400. a) How many must sign up for the package for all costs to be covered? b) If the bus is filled, how much profit will the club make? c) If the student government agrees to cover any loss up to $400, what is the minimum number of participants required?

Solve the following problem using the Contribution Margin Approach. Alpha Corp. expects to operate at 80% of capacity next year. Its forecast operating budget is: a) What is Alpha's break-even revenue? b) What would be Alpha's net income if it operates at full capacity?

Determine the slope and y-intercept of each of the following equations: -0 = 2400 - 4a - 5b