###### Essential Mathematics for Economics and Business

197 SOLVED PROBLEMS

Question: 2.24

## Pocket money, £15, may be spent on either pool (60p per hour) or skating (£1.20 per hour). (a) Write down the equation of the budget constraint. Graph the constraint. (b) Show by calculation and graphically how the budget constraint changes when: (i) The price of pool increases to 75p, the other ...

(a) Let x = number of hours of pool, P_X[/l...
Question: 3.3

## Given the simultaneous equations 2x + 3y = 0.75 (1) 5x + 2y = 6 (2) Solve for x and y algebraically. ...

In these two equations, neither the x- nor the y-t...
Question: 6.17

## Find the turning points for the curve, y=−x³ + 9x² − 24x + 26. Determine which point is a maximum and which is a minimum by using the second derivatives. ...

The graph of y = −x³ + 9x² − 24x + 26 is drawn in ...
Question: 4.20

## Use the log rules to simplify the following expressions to a single term, if possible:(a) logb(25) + logb(70) – logb(55) (b) 4 logx (7) – 3 logx (0.85) + logx (10) (c) 12 logb(12) + 3 logx (8.25) – 2 logb(5) Then evaluate each expression if b = 3, x = e. ...

(a) log_b (25) + log_b (70)  –  log_b (55)[...
Question: 1.8

## (a) A book is priced at US$20. Calculate the price of the book in (i) Euros, (ii) British pounds and (iii) Australian dollars correct to four decimal places. (b) Convert (i) 500 Australian dollars and (ii)$10 000 Singaporean dollars to pounds sterling. ...

The calculations (correct to four decimal places) ...
Question: 9.7

## Solve the following equations by Gaussian elimination: x + y − z = 3 (1) 2x + y − z = 4 (2) 2x + 2y + z = 12 (3) ...

All three equations must be written in the same fo...
Question: 9.20

## Given the input/output table for the three-sector economy: ...

Step 1: Use the underlying assumption total input=...
Question: 9.18

## (a) Find the inverse of the matrix D = (1 0 -2 2 2 3 1 3 2) (b) Show that DD^0−1 = I. ...

(a) Use the definition of the inverse given in equ...
Question: 9.17