Find the values of x and y that minimize the objective function 3x+4y

Question

Find X and Y

(0,8)

(1,4)

(4,1)

(7,0)

Answer 1

If I am interpreting your question correctly, you are given the four (x,y) points listed and then are being asked which among the four gives the smallest value for the objective function shown.

If that is the case, then what you need to do is to take each point, substitute its x and y values into the objective function and calculate the sum of the two terms. So you will get four sums (one for each pair of x, y) so then you just choose for the final answer the x and y used in whichever sum is the smallest.