this is a decision analysis question please help
in Other Math Topics by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

The graph shows the constraints as red lines. The inequalities are represented by areas, and the areas are defined by the constraints. The open area ABOVE both red sloping lines, to the right of x=2 and above the x-axis is the region where the inequalities are true, including the point where they intersect and all points on the lines themselves. 

(The lines intersect where the system 2x+4y=16 (that is, x+2y=8) and 4x+3y=24 is solved. So we can write 4(8-2y)+3y=24, 32-8y+3y=24, 5y=8, y=1.6 and x=8-2y=8-3.2=4.8. The intersection point (4.8,1.6) is shown.)

The blue line is of the form 6x+3y=a, a constant. The minimum point for 6x+3y is when a has the smallest value, and that’s where the blue line is as far over to the left as possible so as to lie within the constraints. This is where x=2 on 4x+3y=24, so 3y=24-8=16, and y=16/3. Therefore a=12+16=28, and the blue line has the equation 6x+3y=28. The minimum value of 6x+3y=28.

by Top Rated User (646k points)
reshown by

Related questions

1 answer
asked Sep 17, 2013 in Other Math Topics by khushi | 167 views
1 answer
Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
82,950 questions
87,618 answers
4,309 users