Solve the following linear programming problem. Restrict x 2 0 and y > 0.Maximize f = 6x + 8y subject toX + y < 82x + y s 14y < 4.Step 1We want to maximize the function f = 6x + 8y subject toX + y s 82x + y < 14y < 4X2 0, y 2 0.We start by graphing the feasible region given by the set of inequalities. Thus, we graph the equationsx + y = 8, 2x + y = 14, and y = 4 as --Select--- v lines. Notice that the test point (0, 0) ---Select---all of the given inequalities, so the solution of the constraint system is the region on or ---Select--- v thelines, in the first quadrant (since x 2 0, y 2 0).20Clear All191817Delete161514Fill131211108No7Solution25 69101112 13 14 15 16 17 18 19 20e HelpWebAssign. Graphing Tool

Name: Solve the following linear programming problem. Restrict x 2 0 and y
Uploaded: 2024-03-20T07:07:26.000Z
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Description: Solve the following linear programming problem. Restrict x 2 0 and y > 0.Maximize f = 6x + 8y subject toX + y < 82x + y s 14y < 4.Step 1We want to maximize the function f = 6x + 8y subject toX + y s 82x + y < 14y < 4X2 0, y 2 0.We start by graphing

Step:-1 Given that Maximize f = 6x + 8y subject tox+y≤82x+y≤14y≤4x, y≥0 First we solve all inequalities by assuming these inequalities as equations. So we have x+y=82x+y=14y=4 Step:-2 Now, for these equations first take one variable ( either x or y) equal to zero and then find other values then take second variable equal to 0 and find value. For equation x+y=8Take x=0 then y=8when y=0 then x=8So, point is (8, 8) Similarly, doing for remaining equations we have equation when x=0 then y when y=0 then x (x, y) x+y=8 y=8 x=8 (8, 0), (0, 8) 2x+y=14 y=14 x=7 (7, 0), (0, 14) y=4 y=4 y=4 line Now, denotes these points on x y- axis and draw a line passes through (8, 0), (0, 8) and a line passes through(7, 0), (0, 14) and y=4 line. Step:- 3 Now, the required common region is OABCD Step:-4 Now, Solving equation x+y= 8 and y=4 for point B and equation x+y=8 and 2x+y=14 for point C. B is (4, 4) and C is (6, 2). Now, check value of f at each boundary point to get maximum value of f.Step:-5 Point f= 6x+8y value of f O (0, 0) f= 6×0+8×0=0 0 A (0, 4) f= 6×0+8×4=32 32 B (4, 4) f= 6×4+8×4=56 56 C (6, 2) f= 6×6+8×2=52 52 D (7, 0) f= 6×7+8×0=42 42 Maximum value of f is 56 at point (4, 4). step:-6 Note:- I don't know i have to fill the blanks in given paragraph of step 1 of problem as you don't mention anything about it, assuming this part of problem. Thank you we graph the equations as independent lines. Notice that the test point (0, 0) satisfies all the given inequalities, so the solution of the constraint system is the region on or below the lines.