This is the task we started in class after the quiz. It is your opportunity to learn by using a linear system to answer a real business question: what price should a restaurant chain charge for a doll?
Provide all answers for this task on graph paper.
Answers for this task are not on this page: we check our work together in the Supply and Demand Debrief at the start of the next class, and the worked solutions are there too.
TIP
If you would rather work from paper, use the Print button on this page, or open the handout directly:
NOTE
If you were away from class, you may print and use this sheet to get started. It has a large grid with the axes already set up for Questions 1 and 2:
Introduction
Supply and demand problems are common for businesses.
For a desirable product, setting the price too low will result in increased demand that may be higher than the supply of the product that is available, leading to shortages, which are viewed poorly by consumers.
If the price is set too high, demand from consumers may be artificially lowered, leading to poor sales: not enough product will be sold, and profits (if there are any) will be slim.
Businesses are looking for the equilibrium point: the price to set for a product so that the supply of a product and the demand for a product are equal.
Case study: BurgerRama cartoon dolls
Joan King is marketing director for the BurgerRama fast food restaurant chain. BurgerRama has decided to have a cartoon-character doll made to sell at a premium price at participating BurgerRama locations. BurgerRama’s supplier has offered several different versions of the doll that could be sold at different prices. The marketing director’s problem is to decide which selling price will best suit the needs of BurgerRama customers and store managers. King has data from previous similar promotions to help her make a decision.
| Selling Price of Each Doll | Number Supplied per Week per Store | Number Requested per Week per Store |
|---|---|---|
| $1.00 | 35 | 530 |
| $2.00 | 130 | 400 |
| $4.00 | 320 | 140 |
Question 1
Use the data from the table to plot points representing selling price and the number of dolls supplied (supply) on a graph. (Selling Price of Each Doll should appear on the -axis, and Number of Dolls Per Week per Store should appear on the -axis.) Draw the line through the data points, and write the word “Supply” on this line.
Question 2
Plot points representing selling price and number of dolls requested (demand) on the same graph. Draw the line through these points. Write the word “Demand” on this line.
Question 3
Use your graph to answer the following questions.
a) If King sets the price at $2.50 per doll, how many disappointed customers will each store have during the week?
b) If King sets the price at $3.80 per doll, how many unsold dolls will remain at each store at the end of a week?
c) According to this graph, if the company could give the dolls away, how many would each store need per week?
d) According to this graph, what price would make the doll supply so tight that the average number available to each store would be zero?
e) Estimate the price where supply and demand will be in equilibrium.
Question 4
Use two of the points given to find an equation that relates , the number of dolls supplied, to , the price of a doll. To do this, you will need to use skills from grade 9. Optionally, consult the handout provided (Finding the Equation of a Line).
Question 5
Use two of the points given to find an equation that relates , the number of dolls in demand, to , the price of a doll.
Question 6
You now have two equations: one that relates supply to price, and another that relates demand to price. Solve this linear system. What price, , will result in demand and supply, , being equal?
NOTE
Do your best on this task. There are no math skills required that you have not already learned. It may take a while to remember how to do something (like finding the two equations), but you can do it. Good luck!
TIP
This may be a useful reference while completing Questions 4 and 5:
Curriculum connection
B1.2
solve problems that arise from realistic situations described in words or represented by linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method (Sample problem: The Robotics Club raised $5000 to build a robot for a future competition. The club invested part of the money in an account that paid 4% annual interest, and the rest in a government bond that paid 3.5% simple interest per year. After one year, the club earned a total of $190 in interest. How much was invested at each rate? Verify your result.).
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B1.4
develop the formula for the slope of a line (i.e., ), and use this formula to determine the equations of lines, given information about the lines (e.g., a graph of a line, a table of values, the coordinates of two points);
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Mathematical processes
Representing
create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
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