Determine the intercepts of the line.
1 answer:
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We can solve this problem by calculating the individual rate of working and equate it to their total rate of working.
If Dave can complete a sales route in 4 hours, then his working rate is
Also, if James can do it in 5 hours, then his working rate is
Let
be the hours that both will use to complete the sales route,
Then rate at which both completes this task is
Meaning if we add their individual rates we should get
That is;
The LCM is
So let us multiply through with the LCM.
We simplify to get,
Dividing through by 9 gives;
Therefore the two will complete sales route in
hours.
If Dave can complete a sales route in 4 hours, then his working rate is
Also, if James can do it in 5 hours, then his working rate is
Let
be the hours that both will use to complete the sales route,
Then rate at which both completes this task is
Meaning if we add their individual rates we should get
That is;
The LCM is
So let us multiply through with the LCM.
We simplify to get,
Dividing through by 9 gives;
Therefore the two will complete sales route in
hours.
Answer:
The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.
Step-by-step explanation:
This is a optimization with restrictions problem.
The restriction is that the perimeter of the square cross section plus the length is equal to 108 inches (as we will maximize the volume, we wil use the maximum of length and cross section perimeter).
This restriction can be expressed as:
being x: the side of the square of the cross section and L: length of the package.
The volume, that we want to maximize, is:
If we express L in function of x using the restriction equation, we get:
We replace L in the volume formula and we get
To maximize the volume we derive and equal to 0
We can replace x to calculate L:
The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.