Download Mock Test One - (1.1-1.5)

Sept. 21, 2016
Mock Test One - (1.1-1.5)
Note: This mock midterm contains problems similar to those students will face on tests in
Math 121. This test was written by the SSS team (not your professors)! It is designed to help
you test yourself on topics covered in class and should not be considered to be a “preview” of
the actual midterm. Note that not all topics covered in your course will necessarily be covered
here. Also, your Math 121 midterms will contain space on the page for you to write your
answers in.
1. Eric, Amy and Mary have started a business manufacturing duct-tape wallets. Mary has
determined that the daily cost, 𝐶𝐶, of producing wallets can be expressed as a linear
function of the number of wallets produced per day, 𝑞𝑞. Amy observes that it costs $320
to produce 80 wallets, and $500 to produce 140 wallets. They can produce up to 700
wallets per day.
a. Find the rule of correspondence for C as a function of q.
b. What is the variable cost per unit and what are the fixed costs?
c. On Friday, the cost of production was $155. How many wallets were produced?
2. Kaylee’s Farm and Gardening store is known for its garden gnomes, which are
manufactured at the store. The manager has determined the demand relationship to be
the linear function 𝑝𝑝 = −0.06𝑞𝑞 + 16.20, where 𝑝𝑝 is the selling price per gnome and 𝑞𝑞 is
the number of gnomes sold. The manager has been quite happy with the sales because
the gnomes cost her $225 in fixed costs, and the variable cost per gnome is given by
𝑣𝑣 = −0.03𝑞𝑞 + 6. The store has at most 200 gnomes in stock.
a. Find the cost C as a function of the quantity produced, 𝑞𝑞.
b. Determine the revenue R as a function of q.
c. Find the profit P as a function of q and determine the output level 𝑞𝑞 that
maximizes profit.
d. Find the maximum profit.
e. At what selling price is profit maximized?
f. Find the break-even point(s).
g. Sketch the graph of the profit function.
continued over …
Answers at: http://library.usask.ca/sss
3. Beekeepers sell premium honey at the local farmers’ market. If 𝑞𝑞 represents the
number of litres of honey sold, the demand for honey at the farmers’ market can be
modelled by
5𝑞𝑞 + 450
, 0 ≤ 𝑞𝑞 ≤ 50 .
𝑞𝑞 + 10
When the price of honey is $12 per litre, beekeepers bring 10 litres to the market to sell.
Moreover, for each $.3 increase in price, two more litres will be supplied to the market.
𝑝𝑝 =
a. Determine the supply function (as a linear function).
b. Find the equilibrium value of 𝑞𝑞 and the market-clearing price.
c. Sketch the graphs of the supply and demand functions on the same set of axes. Label
the equilibrium value of 𝑞𝑞 and the market-clearing price.
4. Serena, a manager of a plant that manufactures jackets, estimates that when the output
level 𝑞𝑞 is near 0, the variable cost 𝑣𝑣 of making one jacket is $24; when the output level
𝑞𝑞 is 20, the variable cost per jacket is $21. For very large batches, this cost is known to
decrease towards $15.
a. Write the variable cost per unit, 𝑣𝑣, in terms of 𝑞𝑞, the number of jackets produced,
assuming that variable cost function is a linear-to-linear rational function of 𝑞𝑞.
b. If the fixed costs are $120, find the total cost 𝐶𝐶 as a function of 𝑞𝑞. (Hint: 𝐶𝐶 will be
a quadratic-to-linear function.)
5. The owner of a small sporting goods store reviewed the records for the sales of his
specially-insulated water bottles during the last year. He noticed that the most bottles
he ever sold in a week were 80. At that time the price per bottle was $9.00, which is as
low as he can go. Alternatively, when he raised the price per bottle to $25.00, no water
bottles were sold at all. Determine the demand p as a quadratic function of q, with the
vertex at (80, 9).
These questions have been adapted from Mathematical Analysis for Business and Economics (Schelin and Bange) and past
mock term tests.
Answers at: http://library.usask.ca/sss