Question

here is a pdf of a test question i need help correcting to get half the points back. please help.

Answer 1

i guess what i need help with is equations to get started? word problems and i do not get along.

Answer 2

Wait hold on

Answer 3

ok

Answer 4

still here?

Answer 5

Haha wait, i got stuck =(

Answer 6

no problem, i got stuck too

Answer 7

well failed it

Answer 8

Let the number of Hot sites be H
Let the number of Cold sites be C

Form the 2 eqns, pertaining to number of hours,
For hours for layout changes, 12 = 1.5H +C ----(1)
For hours for content changes, 16 = H+2C -----(2)

Then form a thrid eqn, for profits, P
P = 50H +250C ----(3)

Now u want to find maximum profits, thus u want to differentiate eqn (3) but there are 2 variables so its going to be hard. So just use eqn (1) and (2) to make another equation,
(1) 12= 1.5H +C
(2) 16= H+2C => 12= H+2C-4
Equate both together:
1.5H +C = H+2C-4
1.5H -H = 2C-C-4
0.5H= C-4
H= 2C-8
differentiate it
dH/dC = 2

Now (3)
P = 50H +250C, differentiate it w.r.t C ( you will know why in a second)
dP/dC = 50 (dH/dC) + 250

Substitute the above dH/dC = 2, into dP/dC

dP/dC = 50 (dH/dC) + 250
dP/dC = 100+250 = 350

Answer 9

This is where im stuck at already.

Answer 10

let me look for a second, in the pencil on the right are the steps in order the professor wrote after the test if that helps any

Answer 11

i think you are on the right track, but i am not sure where to go from there either

Answer 12

yea its either i made a mistake or what, if not the result i got above doesnt make sense -.-

Answer 13

well i do know that i have to graph it, shade the feasible region, and then define the point

Answer 14

Omg this is not calculus question. Woops totally misunderstand the question. okay. i got it.

The graph u draw is correct. Just look at the Graph and see the 2 lines intersect. The region u shade is also correct. in this region there are 4 possible points these are your corners. Obviously the corner (0,0) is wrong. There are 3 other possible choices. So just plug in those 3 points and find which profit is the most.

Answer 15

that's what i don't know how to do is plug in the coords to the problem, and he thinks that i didn't define constraints, did't list profit, didn't list corners, or interpret the problem

Answer 16

because it is difficult for me to draw a graph to illustrate to u. i try my best to describe.
Step by step.
Defining the constraints, means to state the restriction, which are the 2 eqn

Form the 2 eqns, pertaining to number of hours,
For hours for layout changes, 12 = 1.5H +C ----(1)
For hours for content changes, 16 = H+2C -----(2)

This will show that u have adequately considered the problems, and thus come out with a proper solution to go around it.

Next you will have to sketch the 2 lines into the graph which you have done.
You will have to understand that all possible combination of the H and C can be given in the shaded region of the 2 lines (because the answer is bounded by the 2 restrictions/constraints).
Then u must note that the answer can only be in interger value and not decimal or fractional values since u can only have 1,2,3 hot sites but not 1/4 hot sites.
Thus to fit this new constraint, u cannot just take any point in the shaded region, but the corners, because it is at the corners, that H and C will have interger values, the 2 points where the line intersect with the axis and the point where the 2 lines intersect.

Answer 17

ok, wow, i can't believe i actually understand what you wrote instead of the book or professor, unreal

Answer 18

Then how to plug in coordinates into the graph?
Just see which corner u are trying to find first. Then lets say(referring to the graph), the leftmost corner. its cuts the y-axis meaning x=0. So u take the formula of the line and then equate x=0 to find the corresponding value, which is the number of hot or cold sites, that will be answer number one. Find the profit, then go on to the next point.

Next point on the intersecting lines. Equate both equations, find out the combination, which should give point (4,6). find profit.

Then do so for the last point. Which ever point has the highest profit. u declare it the answer.

Answer 19

so i take (4,6) and in that 4 equals hot sites and 6 equals cold sites, so 4 would be $100 in hot site and 6 would be $1500 in profit?

Answer 20

Yesh.

Answer 21

ok i think i get it, thank you so much for your time and help

Answer 22

Np!