Chapter ISG, Problem 5.6.7P

a.

To determine

To write an inequality equation.

Answer to Problem 5.6.7P

  $2.25p+2b>90$

Explanation of Solution

Given information:

Each peach smoothie profit is $2.25

Each berry smoothie profit is $2

Number of peach smoothies are 'p'

Number of berry smoothies are 'b'

Total profit of per day is more than $90

Calculation:

Each peach smoothie profit=$2.25

Each berry smoothie profit=$2

Number of peach smoothies=p

Number of berry smoothies= b

Total profit of per day > $90

Then,

Profit constraint

  $2.25p+2b>90$

b.

To determine

To graph the solution of inequality.

  $2.25p+2b>90$

Explanation of Solution

Given information:

  $2.25p+2b>90$

Graph:

  

Calculation:

  $2.25p+2b>90$

Rewriting the equation,

  

Slope intercept form

  

  $slope=-1.125$

Means -1.125 unit change in y-coordinate with respect to 1 unit change in x-coordinate

Y-intercept: (0, 45)

Ordinary equation

  

Substituting p=0

Then b=45

Substituting b=0

Then x=20

Table of p and b is given below

p	b
0	45
40	0

Then graph is given below

  

For the shaded region,

Take a point above the line

Point (20,30) is below line put in inequality equation

  

On solving,

  

On solving,

105>90 is true

The region is above line

Then graph of inequality is given below

  

c.

To determine

To find number of berry smoothies on Monday.

Answer to Problem 5.6.7P

22.5 or more berry smoothies sold on Monday.

Explanation of Solution

Given information:

  $2.25p+2b>90$

20 peach smoothies sold on Monday

Calculation:

Number of peach smoothies sold on Monday, p=20

Then number of berry smoothies sold on Monday, b

  $2.25p+2b>90$

On solving,

  $45+2b>90$

On solving,

  $2b>45$

On solving,

  $b>22.5$

Hence, 22.5 or more berry smoothies sold on Monday.

d.

To determine

To find minimum number of smoothies sold on Tuesday to made daily goal.

Answer to Problem 5.6.7P

Minimum 40 smoothies will be sold.

Explanation of Solution

Given information:

  $2.25p+2b>90$

Calculation:

For making daily goal by minimum number of smoothies sold

Then to sold peach smoothies and not sold berry smoothies

Means

b=0

Substituting values of b in inequality equation

  $2.25p+2(0)>90$

On solving,

  $2.25p>90$

On solving,

  $p>40$

Hence, minimum 40 smoothies will be sold.