By graphing the system of constraints find the values of x and y that maximize the objective function x+y< =82x+y< =10x=> 10y=> 0 a. (0,0) b. (5,0) c.(0,8) d.(2,6)

D(2,6)

Step-by-step explanation:

To find  the values of x and y that maximize the objective function

x+y≤8....(line 1)

2x+y≤10.......(line 2)

x≥0......(3)

y≥0.......(4)

we need need to plot them by the following steps.

Step 1: Find coordinates(x,y) of line(1) x+y=8

Put x=0 , we get y =8

Put y=0, we get x=8

by this we got points (0,8) and (8,0) to plot line (1)........(a)

Step 2: Find coordinates (x,y) of line(2) 2x+y=10

Put x=0 , we get y =10

Put y=0, we get 2x=10⇒x=5

by this we got points (0,10) and (5,0) to plot line (2)...........(b)

so with the help of (a) , (b) ,(3) and (4) ,we plot the given graph .

By the graph we can find  that at (x,y)=(2,6) the objective function is maximized , so option D is right.

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step-by-step explanation: