Answer:
Ruhana and her team should refurbish 15 tv sets and 20 dvd players each week to minimize the cost.
Step-by-step explanation:
For the given situation let the number of tv sets be x and number of dvd players be y.
Now we have to minimize the cost as it costs $75 to refurbish a tv set and $40 to refurbish a dvd player.
i.e. Minimize z=75x+40y
it gives subject to the constraints
4x+2y≥100......(1)(100 hours each week. It takes 4 hours to refurbish a tv set and 2 hours to refurbish a dvd player.)
x+y≥35.......(2)(weekly sales target is to refurbish at least 35 tv sets or dvd players.)
To plot equation (1) we need to find coordinates of points lying on line (1)
put x=0 gives 2y=100⇒y=50
put y=0 gives 4x=100⇒x=25
So we got points (0,50) and(25,0) for (1)..............(3)
Similarly for equation (2)
put x=0 gives y=35
put y=0 gives x=35
so we got points (0,35) and(35,0) for (2).................(4)
with the help of (3) and (4) we plot the following graph (assume x≥0 and y≥0)
The unbounded feasible region determined by constraints gives the corner points as A(0,50),B(15,20)and C(35,0).
from we get the value of z is minimum at point B (15,20) .
hence we got our optimal solution at B (15,20), where x is the number of tv sets and y is the number of dvd players .therefore Ruhana and her team should refurbish 15 tv sets and 20 dvd players each week to minimize the cost.
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