MATHEMATICS 201-103-RE
23 – APPLICATIONS TO
BUSINESS AND ECONOMICS
PHILIP FOTH
1. The cost function is given by C (q)  900  20q  q 2 .
(a) Find the average cost and marginal cost functions.
(b) The minimum average cost and the corresponding production level.
2. The cost function is given by C (q)  3200  8 q  0.1q3/2 . Find the minimum average cost
and the corresponding production level.
3. The average cost of producing q units of a commodity is given by
3000
c(q ) 
 80  0.02 q  0.000005 q 2 .
q
Find the marginal cost at a production level of 1000 units. What is its practical meaning?
4. The cost function is given by C (q)  4000  6 q  0.006 q 2 and the demand is given by
p  20  0.002 q . Find the production level that maximizes profit.
5. A basketball stadium has 23000 seats. When the tickets were sold at 50$, the average
attendance was 14000 . When the ticket price was lowered to 45$, the average attendance rose to
16000 . Assuming the dependence is linear, what ticket price will maximize revenue?
6. Jean-Claude is selling jars of honey at a local farmers’ market. If he charges 12$ for a jar, he
sells 30 jars per day. For each increase in price by 1$, Jean-Claude loses two sales per day.
Assuming each jar costs him 7$, what should be his selling price to maximize his profit?
7. An apartment complex has 150 identical units. If the manager charges 800$ per months, all
units are occupied. For each 20$ increase in rent, three units will become vacant. What rent
should the manager charge to maximize revenue?
8. The demand function is given by p  200  0.04 q . Find the elasticity of demand
corresponding to the price of 85$. Is the demand elastic or inelastic? Should the price be raised
or lowered to increase revenue?
9. The price p of a motorcycle is related to the quantity q that can be sold by the equation
p  e0.002 q  60000 . Find the price for which elasticity equals 0.8.
10. Suppose that the demand and price are related by the equation p  17 q  680 . Find the
elasticity as a function of q . What price makes it unit elastic?
11. A baker found that the price p of a loaf of bread is related to the demand q by the equation
q3/2  1800  ln  0.2 p   1000 . At the price of 5$, is the demand elastic or inelastic? Should the
price be lowered or raised? Find the price that maximizes revenue.
12. The demand equation is given by
demand is elastic.
p  1200  8 q 2 . Find the values of q for which the
13. A restaurant sells 900 bottles of a particular wine annually at a constant rate. It costs the
restaurant 4$ per year to store each bottle and 200$ in fixed order costs. To minimize costs, how
often should the restaurant order this wine and how many bottles should be in each order?
14. A supermarket sells 600 cases of flour at a steady rate during a given year. It costs 5$ to
store one case for a year and the handling cost for each delivery is 120$. What is the optimal
number of cases in each order that minimizes costs?
ANSWERS
1. (a) c(q) 
900
 20  q , C(q)  20  2q
q
(b) 80 $/unit, 30 units
3. 105 $/unit, predicts the cost of producing the 1001st unit.

80  2 q
12. q  0, 5 2
q

4. 875 units 5. 42.50 $
8.  0.74 , inelastic, increase the price 9. 60000  e5/4  17190 $
6. 17 $ 7. 900 $
10. E (q) 
2. 14 $/unit, 1600 units
,
680
$
3
11. Elastic, decrease the price, 5e1/9  4.47 $
13. Every four months, 300 bottles.
14. 120 2  170