M40-98

Two methods By which we can solve this question

1. Basic Method:

just take the cases out
1. Price: 32$, Shoes: 80 this gives the revenue as 2560$
2. Price: 30$, Shoes: 100 this gives the revenue as 3000$
3. Price: 28$, Shoes: 120 this gives the revenue as 3360$
4. Price: 26$, Shoes: 140 this gives the revenue as 3640$
5. Price: 24$, Shoes: 160 this gives the revenue as 3840$
6. Price: 22$, Shoes: 180 this gives the revenue as 3960$
7. Price: 20$, Shoes: 200 this gives the revenue as 4000$
8. Price: 18$, Shoes: 220 this gives the revenue as 3960$(the amount starts to reduce)

so max revenue we can get from the 7th case i.e 4000$,
By what amount it increase: (4000-2560)$ that comes out to be 1440$



2. 2nd Method

By using maxima/Minima Concept

We can form the equation as Revenue = (80+20x) * (32-2x) [X is the number of iteration)
for max min, differentiation of the equation must be zero
hence,
Revenue = -40x^2-160x+640x+2560 = revenue
hence,
dr/dx = -80x+480 = 0
so x=6

so Revenue by putting x in the equation comes out be: 4000$
By what amount it increase: (4000-2560)$ that comes out to be 1440$