We start by setting out the inequalities
Let the number of kennels is 'k' and the number of dogs is 'd'
Inequality 1:
30 minutes per dog + 10 minutes per kennel ≤ 7 hours
30d + 10k ≤ (7 × 60)
30d + 10k ≤ 420
Inequality 2:
Number of kennels to be cleaned is 30
k ≤ 30
Inequality 3:
Number of dogs to bathe is 10
d ≤ 10
Sketching the graph on the Cartesian axes will look like the diagram below
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PART A
From the graph, we can see two intersection coordinates that satisfy the three inequality, which we will check in turn for the greatest possible money that Nikolai could earn
First coordinate (18, 8) ⇒ This means, 18 kernels and 8 dogs
(18 × $3) + (8 × $10) = 54 + 80 = $134
Second coordinate (30, 4) ⇒ This means, 30 kernels and 4 dogs
(30 × $3) + (4 × $10) = $90 + $40 = $130
The maximum earning Nikolai could get is $134 if he cleans 18 kernels and baths 8 dogs.
-----------------------------------------------------------------------------------------------------------PART B
If Nikolai cleans all the kernels first, he'd spend 30 × 10 minutes = 300 minutes out of 420 minutes he has in total in a day
He'd have 420 - 300 = 120 minutes left to bath some dogs.
He needs 30 minutes to bath one dog
With 120 minutes he's got left, he can only bath 120 ÷ 30 = 4 dogs
Let the number of kennels is 'k' and the number of dogs is 'd'
Inequality 1:
30 minutes per dog + 10 minutes per kennel ≤ 7 hours
30d + 10k ≤ (7 × 60)
30d + 10k ≤ 420
Inequality 2:
Number of kennels to be cleaned is 30
k ≤ 30
Inequality 3:
Number of dogs to bathe is 10
d ≤ 10
Sketching the graph on the Cartesian axes will look like the diagram below
---------------------------------------------------------------------------------------------------------------
PART A
From the graph, we can see two intersection coordinates that satisfy the three inequality, which we will check in turn for the greatest possible money that Nikolai could earn
First coordinate (18, 8) ⇒ This means, 18 kernels and 8 dogs
(18 × $3) + (8 × $10) = 54 + 80 = $134
Second coordinate (30, 4) ⇒ This means, 30 kernels and 4 dogs
(30 × $3) + (4 × $10) = $90 + $40 = $130
The maximum earning Nikolai could get is $134 if he cleans 18 kernels and baths 8 dogs.
-----------------------------------------------------------------------------------------------------------PART B
If Nikolai cleans all the kernels first, he'd spend 30 × 10 minutes = 300 minutes out of 420 minutes he has in total in a day
He'd have 420 - 300 = 120 minutes left to bath some dogs.
He needs 30 minutes to bath one dog
With 120 minutes he's got left, he can only bath 120 ÷ 30 = 4 dogs