Need with this asap! analysis question involving math

  2000 of Type A; 3000 of Type B; profit of $74 million

You have enough of these similar questions that it seems like it would pay to find a generic solution.

Let revenue (R) be ...

  R = ax + by

and cost (C) be ...

  C = cx² +dxy +ey² +fx +gy +h

Then profit (P) is the difference between revenue and cost ...

  P = R - C = ax + by - (cx² +dxy +ey² +fx +gy +h)

  P = -cx² -dxy -ey² +(a-f)x +(b-g)y -h

The maximum is found where the partial derivatives with respect to x and y are zero.

  ∂P/∂x = -2cx -dy +(a-f) = 0

  ∂P/∂y = -dx -2ey +(b-g) = 0

These two equations can be written in standard form as ...

  2cx +dy = a-f

  dx +2ey = b-g

Then Cramer's rule gives the generic solution to this linear system as ...

  x = (d(b-g) -2e(a-f))/(d² -4ce)

  y = (d(a-f) -2c(b-g)/(d² -4ce)

Using your numbers ...

  {a, b, c, d, e, f, g, h} = {4, 6, 1, -3, 9, 9, -42, -7}

we get ...

  x = (-3(6-(-42)) -2·9(4-9))/((-3)² -4·1·9) = (-3·48 -18(-5))/-27 = -54/-27 = 2

  y = (-3(-5) -2·1·48)/-27 = -81/-27 = 3

And the profit is ...

  P = -1(2²) +3(2)(3) -9(3²) -5(2) +48(3) +7 = -4 +18 -81 -10 +144 +7 = 74

Sale of 2000 type A units and 3000 type B units will yield the maximum profit of $74 million.

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕