Consider the domain S ⊂ R2, determined by the following system of inequalities: x + 5y...
Consider the domain S ⊂ R2, determined by the following system
of inequalities:
x + 5y ≤ 5 ,2x + y ≤ 4 ,x + y ≤ 15 ,x ≥ 0, y ≥ 0
a) Sketch the domain S b) Find the coordinates of all “corners”
(vertices of the boundary) of S c) Determine the maximum value on S
of the function z = f(x,y) = 3x + 5y. If you think that a maximum
value does not exist, explain why. d) If you think that a maximum
value exists, determine the point or points at which it occurs (is
achieved).
Homework Answers
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Consider the domain S ⊂ R2, determined by the following system
of inequalities:
x + 5y...
(a) Consider the minimisation and maximisation of the objective function f : R2 + R given...
(a) Consider the minimisation and maximisation of the objective function f : R2 + R given by f(x,y) = (x - 1)2 + y2 +3 on the feasible region D C R2 consisting of the boundary and interior of the right-angled trian- gle whose vertices are the points (0,0), (3,0) and (0,4). (0) Make a sketch on the coordinate plane Rd of the region D and add to your sketch a few contours of the objective function f. (ii) Obtain...
Solve the following linear programming problem. Maximize: z= 3x + 4y subject to: 2x + 5y...
Solve the following linear programming problem. Maximize: z= 3x + 4y subject to: 2x + 5y = 10 6x + y s 10 X20, y20 The maximum value is The maximum occurs at the point (Type an ordered pair. If the maximum occurs at more than one point, type either answer. Type an integer or a fraction.)
Consider the minimisation and maximisation of the objective function f : R2 + R given by...
Consider the minimisation and maximisation of the objective function f : R2 + R given by f(x, y) = (x - 1)2 + y2 + 3 on the feasible region DC R2 consisting of the boundary and interior of the right-angled trian- gle whose vertices are the points (0,0), (3,0) and (0,4). (iv) Find the coordinates (x*, y*, 1*) of the stationary point of your function L(x, y, 1). (v) State if the point (x*,y*) is a constrained minimum of...
Include all relevant work please. s. Consider f(x) = *** a. Find the domain. [3] b....
Include all relevant work please.
s. Consider f(x) = *** a. Find the domain. [3] b. Find any vertical asymptotes. [3] c. Determine if there are any holes. If so, give the coordinates of the hole. [2] d. Find any horizontal or oblique asymptotes. [3] e. Determine if the graph intersects a horizontal/oblique asymptote, if it exists. Show work! [3] f. Sketch a graph of the function. To receive full credit, label any x and y intercepts and the asymptotes....
SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY THE CRAMER'S METHOD 3X+5Y+3Z-12 2X+5Y-2Z-6 3x+6Y+3Z-3 a) X Y b) CHEC...
SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY THE CRAMER'S METHOD 3X+5Y+3Z-12 2X+5Y-2Z-6 3x+6Y+3Z-3 a) X Y b) CHECK YOUR RESULTS. (USE MATRICE FUNCTIONS, PRESS F2. AND THEN PRESS CTRL+SHIFT+ENTER) 3IF Y-SINC) EXPOO. INTEGRATE Y FROM X-0 Tox-1. COMPARE WITH REAL VALUE IF DX-0 a) INT b) INT ,IF DX- 005 REAL VALUE 3) Plot sin x letting maco c/ Prepave hese cuves 4) SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY INVERSE METHOD 3 X+3Z-13 2X +5 Y-2Z-2 3 X+6Y+2Z-3 Z-...
27 -12 points Determine graphically the solution set for the system of inequalities. x + y s 3 2x + ys 5 2x yz-1 x2...
27 -12 points Determine graphically the solution set for the system of inequalities. x + y s 3 2x + ys 5 2x yz-1 x2 0, y 2 0 Tools Actions 1. Select an object from the Tols menu to the left. Delete 2. Enter coordinates Object Properties below, or use the mouse to place and move objects. Fil To enter a fractional or decimal coordinate, use Object Properties. No Soltion View our tutorial videos Object Properties Soloct a Tool...
Solve the following linear inequalities. Give answers in interval notation a) -2x+S>23 S-2x c) ts프>x or...
Solve the following linear inequalities. Give answers in interval notation a) -2x+S>23 S-2x c) ts프>x or 3x+621 d) 3x+ 3 S-3 and 4x +2>2 Find the slope-intercept form of the line which passes through the given points a) P(2, 3) Q(-6,0) b) P(4,7) 0(7.7)
1: Solve the following inequalities and express your answer in interval notation. (10 points) x? -...
1: Solve the following inequalities and express your answer in interval notation. (10 points) x? - 5x-620 Solution 1: 2: Solve the absolute value inequality; 3 - 2x > 9. Write the solution in interval notation. (10 points) Solution 2: (5 points each) 3: For the following function, 3x + 4 f(x)= x+2 3.1: State the domain of the function, Solution 3.1: 3.2: Find x- and y-intercepts (if any), Solution 3.2: 4: Given f(x)=x+5x+2, evaluate the following expression: f(x+h)-f(x) +0....
Solve the following linear programming problem. Maximize: z-14x+10y subject to: 3x+5y s15 7x +y s 15 x20, y20 The maximum value is The maximum occurs at the point Type an ordered pair. If the maximum...
Solve the following linear programming problem. Maximize: z-14x+10y subject to: 3x+5y s15 7x +y s 15 x20, y20 The maximum value is The maximum occurs at the point Type an ordered pair. If the maximum occurs at more than one point, type either answer. Type an integer or a fraction.)
Solve the following linear programming problem. Maximize: z-14x+10y subject to: 3x+5y s15 7x +y s 15 x20, y20 The maximum value is The maximum occurs at the point Type an...
Consider the minimisation and maximisation of the objective function f : R2 + R given by...
Consider the minimisation and maximisation of the objective function f : R2 + R given by f(x,y) = (1 - 1)2 + y2 + 3 on the feasible region D C R2 consisting of the boundary and interior of the right-angled trian- gle whose vertices are the points (0,0), (3,0) and (0,4). (a) Write down a Lagrangian function L(x, y, 1) whose only stationary point (x*, y*, \*) corre- sponds to the point of tangency (r*, y*) between the line...
(a) Consider the minimisation and maximisation of the objective function f : R2 + R given by f(x,y) = (x - 1)2 + y2 +3 on the feasible region D C R2 consisting of the boundary and interior of the right-angled trian- gle whose vertices are the points (0,0), (3,0) and (0,4). (0) Make a sketch on the coordinate plane Rd of the region D and add to your sketch a few contours of the objective function f. (ii) Obtain...
Solve the following linear programming problem. Maximize: z= 3x + 4y subject to: 2x + 5y = 10 6x + y s 10 X20, y20 The maximum value is The maximum occurs at the point (Type an ordered pair. If the maximum occurs at more than one point, type either answer. Type an integer or a fraction.)
Consider the minimisation and maximisation of the objective function f : R2 + R given by f(x, y) = (x - 1)2 + y2 + 3 on the feasible region DC R2 consisting of the boundary and interior of the right-angled trian- gle whose vertices are the points (0,0), (3,0) and (0,4). (iv) Find the coordinates (x*, y*, 1*) of the stationary point of your function L(x, y, 1). (v) State if the point (x*,y*) is a constrained minimum of...
Include all relevant work please.
s. Consider f(x) = *** a. Find the domain. [3] b. Find any vertical asymptotes. [3] c. Determine if there are any holes. If so, give the coordinates of the hole. [2] d. Find any horizontal or oblique asymptotes. [3] e. Determine if the graph intersects a horizontal/oblique asymptote, if it exists. Show work! [3] f. Sketch a graph of the function. To receive full credit, label any x and y intercepts and the asymptotes....
SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY THE CRAMER'S METHOD 3X+5Y+3Z-12 2X+5Y-2Z-6 3x+6Y+3Z-3 a) X Y b) CHECK YOUR RESULTS. (USE MATRICE FUNCTIONS, PRESS F2. AND THEN PRESS CTRL+SHIFT+ENTER) 3IF Y-SINC) EXPOO. INTEGRATE Y FROM X-0 Tox-1. COMPARE WITH REAL VALUE IF DX-0 a) INT b) INT ,IF DX- 005 REAL VALUE 3) Plot sin x letting maco c/ Prepave hese cuves 4) SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY INVERSE METHOD 3 X+3Z-13 2X +5 Y-2Z-2 3 X+6Y+2Z-3 Z-...
27 -12 points Determine graphically the solution set for the system of inequalities. x + y s 3 2x + ys 5 2x yz-1 x2 0, y 2 0 Tools Actions 1. Select an object from the Tols menu to the left. Delete 2. Enter coordinates Object Properties below, or use the mouse to place and move objects. Fil To enter a fractional or decimal coordinate, use Object Properties. No Soltion View our tutorial videos Object Properties Soloct a Tool...
Solve the following linear inequalities. Give answers in interval notation a) -2x+S>23 S-2x c) ts프>x or 3x+621 d) 3x+ 3 S-3 and 4x +2>2 Find the slope-intercept form of the line which passes through the given points a) P(2, 3) Q(-6,0) b) P(4,7) 0(7.7)
1: Solve the following inequalities and express your answer in interval notation. (10 points) x? - 5x-620 Solution 1: 2: Solve the absolute value inequality; 3 - 2x > 9. Write the solution in interval notation. (10 points) Solution 2: (5 points each) 3: For the following function, 3x + 4 f(x)= x+2 3.1: State the domain of the function, Solution 3.1: 3.2: Find x- and y-intercepts (if any), Solution 3.2: 4: Given f(x)=x+5x+2, evaluate the following expression: f(x+h)-f(x) +0....
Solve the following linear programming problem. Maximize: z-14x+10y subject to: 3x+5y s15 7x +y s 15 x20, y20 The maximum value is The maximum occurs at the point Type an ordered pair. If the maximum occurs at more than one point, type either answer. Type an integer or a fraction.)
Solve the following linear programming problem. Maximize: z-14x+10y subject to: 3x+5y s15 7x +y s 15 x20, y20 The maximum value is The maximum occurs at the point Type an...
Consider the minimisation and maximisation of the objective function f : R2 + R given by f(x,y) = (1 - 1)2 + y2 + 3 on the feasible region D C R2 consisting of the boundary and interior of the right-angled trian- gle whose vertices are the points (0,0), (3,0) and (0,4). (a) Write down a Lagrangian function L(x, y, 1) whose only stationary point (x*, y*, \*) corre- sponds to the point of tangency (r*, y*) between the line...
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