Chapter ISG, Problem 3.1.2.1P

a.

To determine

Two write an equation

Answer to Problem 3.1.2.1P

Cost and revenue function is $F(x)=75x$ and $C(x)=840+47x$

Explanation of Solution

Given:

Initial investment= $840

Buying and fixing cost= $47

Selling price= $75

Calculation:

Cost function= $C(x)$

Revenue function= $F(x)$

Cost function is,

  $C(x)=840+47x$

Revenue function is,

  $F(x)=75x$

Hence cost and revenue function is $F(x)=75x$ and $C(x)=840+47x$

b.

To determine

To write an equation of a profit $P(x)$

Answer to Problem 3.1.2.1P

  $P(x)=28x-840$

Explanation of Solution

Given:

Initial investment= $840

Buying and fixing cost= $47

Selling price= $75

Calculation:

Let the profit be $P(x)$

  $P(x)=F(x)-C(x)$

Substituting the values,

  $P(x)=75x-(840+47x)$

Solving,

  $P(x)=75x-840-47x$

Hence, equation of profit is

  $P(x)=28x-840$

c.

To determine

To draw the graph of function of profit.

Explanation of Solution

Given:

Initial investment= $840

Buying and fixing cost= $47

Selling price= $75

Graph:

The graph represent: y= 28x - 840

  

d.

To determine

To find profit of 120 bikes

Answer to Problem 3.1.2.1P

120 cycles gives $2520 profit.

Explanation of Solution

Given:

Initial investment= $840

Buying and fixing cost= $47

Selling price= $75

Calculation:

Equation of function,

  $P(x)=28x-840$

Substituting values,

  $P(x)=28(120)-840$

So,

  $P(x)=3360-840$

And,

  $P(x)=2520$

Hence, 120 cycle gives $2520 profit.

e.

To determine

To find breaking point.

Answer to Problem 3.1.2.1P

40 is the breaking point.

Explanation of Solution

Given:

  $P(x)=0$

Calculation:

Substituting values,

  $P(x)=28x-840$

So,

0= $28x-840$

now,

28x = 840

Dividing by 28,

x = 40

40 is the breaking point.