Which term best describes the solution of the situation represented by the system of inequalities? (assume that x is greather than or equal to 0 and y is greater than or equal to 0)

3x+4y is less than or eaual to 8

2x+4y is less than or equal to 6
f(x,y)=x+y

a. alternate optimal solutions
b. one optimal solution
c. unbounded
d. infeasible

The system of Inequality given here is

  1. →x≥0

  2.→y≥0

  3.→3x+4y≤8

   4.→2x+4y≤6

f(x,y)=x+y

Drawing the Inequality on the Coordinate plane and obtaining the feasible points

And Feasible Points are

1.→(0,1.5)

2.→(0,0)

3.→(2.667,0)

4.→(2,0.5)

→f(0,1.5)=0+1.5=1.5

→f(0,0)=0+0=0

→f(2.667,0)=2.667+0=2.667

→f(2,0.5)=2+0.5=2.5

⇒There is one Optimal Solution obtained at Point (2.667,0).

Option B

One optimal solutions

The answer is in the image 

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

The answer is in the image 

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km