Question

An company manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes $3$ hours of wiring and $2$ hours of drilling. Each of fan must go through $2$ hours of wiring and $1$ hour of drilling. During the next production period, $240$ hours of wiring time are available and up to $140$ hours of drilling time may be used.

Each air conditioner sold yields a profit of $E25$. Each fan assembled may be sold for a profit of $E15$. Formulate and solve this linear programming mix situation to find the best combination of air conditioners and fans that yields the highest profit.

Answer 1

Assume that

$x$ is number of air conditioners

$y$ is number of units.

according to question.

wiring $\Rightarrow 3x+1y=240$.......(1)

Drilling $\Rightarrow 2x+y\le 140$

and profit

$z=25x+15y$

minimum air conditioners

$x\ge 20$

minimum term

$0\le y\le 80$

by equation (1) and (2)

$3x+y\le 24-0$

for the graph $x$ will be $x$ and $y$ will be $y$ (Refer image)

$(20,2)$

$(70,0)$

$(20,80)$

$(80,80)$

there four vertices defines the leasible region. check the value of the profit finction at these four points to find the maximum value at $(20,0)$

$Z=25\times 20+0$

$=500$

at $(70,0)$

$Z=1750$

at $(20,80)z=1700$

at $(20,80)z=1950$

maximum profit $z=1950$