An electronics firm manufactures printed circuit boards and specialized electronics devices.

Question

Final assembly operations are completed by a small group of trained workers who labor simultaneously on the products. Because of limited space available in the plant, no more then ten
assemblers can be employed. The standard operating budget in this functional department allows a maximum of $9000 per month as salaries for the workers.
The existing wage structure in the community requires that workers with two or more years of experience receive $1000 per month, while recent trade-school graduates will work for only $800. Previous studies have shown that experienced assemblers produce $2000 in value added per month while new-hires add only $1800. In order to maximize the value added by the
group, how many persons from each group should be employed?
Solve graphically and by the
simplex method.

Answer 1

Lot of verbiage here, ....

number of experienced workers --- x
number of non-exp workers ----- y

condition 1: x + y ≤ 10
condition 2 : 1000x + 800y ≤ 9000
or 10x + 8y ≤ 90

so plot the regions defined by
x + y ≤ 10 and 10x + 8y ≤ 90 on the same grid
a bit of easy algebra will show their boundaries to intersect at (5,5)

Profit = 2000x + 1800y - cost
= 2000x + 1800y - 1000x - 800y = 1000x + 800y
Now any point in the intersection region in the first quadrant would be
value for the profit.
suppose there is a profit of 0, (no workers at all)
then 1000x + 800y = 0
or y = -5x/4 , it would have a slope of -5/4

so "sliding" this line parallel to itself until you reach the farthest point of the region will land at (5,5)
so they need 5 experienced workers and 5 apprentices.

I had no idea what the "simplex method" is as it applies to this type of problem, so I found this youtube, but it looks so weirdly complicated.

www.youtube.com/watch?v=rzRZLGD_aeE&ab_channel=MeghanDeWitt

(copy and paste the URL)