What is the minimum value points of z=30x+40y subject of x+y<=140 x>=45 y>=32 20x+10y>=1500

9514 1404 393

  minimum z: 3050

Step-by-step explanation:

The attached graph shows the feasible region as a white space. The dashed lines at its edges are part of the solution set. The vertex closest to the origin is the one that minimizes z: (x, y) = (59, 32).

The minimum value of z is ...

  30·59 +40·32 = 3050

this is the formula: v = the value of investment at the end of the time period

p = the principal amount (the initial amount invested)

r = the annual interest rate

n = the annual frequency of compounding (how many times a year interest is added)

t = the number of years the money is invested

^ means raise to the power of