Question

A toy company manufactures two types of dolls, A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of Rs 12 and Rs 16 per doll respectively on dolls A and B, how many of each should be produced weekly in order to maximize the profit?

Answer 1

@satellite73 @UnkleRhaukus @karatechopper @Hero

Answer 2

"indicated that the combined production level should not exceed 1200 dolls per week"
\[A+B\leq 1200\]

Answer 3

\[A\leq 3B+600\]

Answer 4

sorry i am unable to view it

Answer 5

\[B\leq \frac{1}{2}A\]

Answer 6

Those are your restrictions and

you need to maximize

\[12A+16B=P\]

Answer 7

can you please tell me how to draw the graph

Answer 8

@Outkast3r09

Answer 9

Looks like @Outkast3r09 provided the equations you need

Answer 10

i know how to do the equations.

Answer 11

So what do you need help with?

Answer 12

@Hero
its the graph.
but i am unable to find its intersection point.
help me with that plz

Answer 13

You want to maximize
12A + 16B = P while adhering to the constraints. So whichever point yields the maximum profit will be your solution.

Answer 14

i know but before that .i'm unable to find that maximum point :(

Answer 15

I found it in two seconds

Answer 16

tell me the process please

Answer 17

Well, basically, all you do is define your profit equation as

f(a,b) = 12a + 16b

then try different points until you find the one that yields the maximum profit

So try:

f(600, 0)
f(800, 400)
f(1050, 150)

One of those will yield the max.

Answer 18

the points at each corner of the shaded area is the possible max profits

Answer 19

so the most simple way would to find out at which what points do those lines cross and then plug them into your profit equation

Answer 20

after that i have to find their intersection point,which i m unable to do

Answer 21

pull the inequality signs out and you'll get the lines, find the intersects by equaling them to each other

Answer 22

from the picture you can see what lines intersect

Answer 23

at c and b

Answer 24

I mean that if you graphed the lines you could see which functions intersect each other... then make those functions equal each other and you'll get the x coordinate of the point of intersection