I need help on this question. I know the answer is \'D\'. However, I just don\'t

Question

I need help on this question. I know the answer is 'D'. However, I just don't undersatnd how they got the numbers 30 for 'x' and 60 for 'y' on the graph. In the example it simply says to find the points where the surface intersects the coordinate or (x,y,z) axis. So how would I find those points?

A clothing company makes a profit of $10 on its long-sleeved T-shirts and $5 on its short-sleeved T-shirts. Assuming there is a $300 setup cost, the profit on T-shirt sales is z= 10x +5y-300. where x is the number of long-sleeved T-shirts sold and y is the number of short-sleeved T-shirts sold. Assume x and y are nonnegative. Complete a. through c. below a. Graph the plane that gives the profit. Choose the correct graph below a. Graph the plane that gzives the proft. Choose On 300 60 30 -100 30 10 x 60 x 60 -300

Explanation / Answer

z = 10x + 5y - 300

We are basically finding the intersections with the xand y axes here

Intersection with the x-axis : This is when y = z = 0

0 = 10x + 5(0) - 300

10x - 300 = 0

10x = 300

x = 300/10

x = 30

So, this is how we get (30,0,0) as the intersection with the x-axis

Intersection with y-axis : This is when x = z = 0....

0 = 10(0) + 5y - 300

5y - 300 = 0

5y = 300

y = 300/5

y = 60

So, the intersection with y-axis is (0,60,0)

Intersection with z-axis :

z = 10(0) + 5(0) - 300

z = -300

So, intersection with z-axis is (0,0,-300)

So, the three intersections of this surface with the x,y and z-axes are :

(30,0,0)

(0,60,0)

(0,0,-300)

This is how we get the answers.

And as you said, option D it is

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