QMDS 100 - Business Mathematics
Solutions to Problem Set
Lecture 1 - Linear and quadratic functions
1. (a). No, the price is not a function of the quantity sold because one domain corresponds more than one range in a function. (b). No. (The reason is the same as (a)).

2. Let [pic] be the no of successful phone calls a) H Regency : Daily income = [pic] MO Hotel : Daily income = [pic] b) [pic] (c). H Regency offers a better wage.

Lecture 2 - Applications of Linear and quadratic functions (1)
1. [pic]

2. S(p) = 5.24p2 – 100

3. [pic]

4. Substituting these data points into the general equation for a quadratic function [pic], and solving the resulting system simultaneously gives the demand function. [pic], where p equals the selling price in dollars and [pic]equals demand stated in thousand of units.

Lecture 3 - Applications of Linear and quadratic functions (2)
1. 250 persons

1. (a). level of output decreases. (b). level of output increases. (c). level of output increases.

3. 4000 units

4. (a). [pic] (b). [pic] (c). [pic] (d). $-9900 (e). 22000 timers

5. Let [pic] be the no of mobile phones produced and sold (a). Cost = 580,000 + 900x; Revenue = 1700x; Profit = 800x – 580,000 (b). break-even point : (725, 1232500) (c). (i) 795 units (ii) 1000 units (iii) 800 units

6. Let [pic] be the no of units of Model 9805C being produced and sold (a). TC(x) = 1383x + 95040 [pic]

(b). break-even point : (1320, 1920600) (c).

[pic] (d). At the sales level of 1320 units, the profit function intersects with the x-axis. This means the profit is zero at that level. (e). 3352 units (integer)

7. (a). u =5 hundred (b). u =15 hundred

8. (a). Max Revenue=9 when