Question #1

Form the dual maximization problem (Usex₁,x₂, andx₃as the variables andfas the function.) and use the simplex method to solve the minimization problem. Assume that all variables are nonnegative.Minimize

g=14y₁+13y₂,

subject to the following.

y1	+	y2		100
2y1	+	y2		140
6y1	+	5y2		580

Maximizef=

subject to

---------------------------		14
-------------------------		13
x1,x2,x3		0	.

The minimum value of the objective function is--------------- which occurs at

(y₁,y₂) = ------------

Question #2

A function and the graph of a feasible region are given.

f=4x+5y

Thexycoordinate plane is given. Two lines and a shaded region are on the graph.

• The linex+ 2y= 19enters the window on the positivey-axisbelow the other line, goes down and right, crosses the line3x+ 2y= 29,and ends on the positivex-axis.
• The line3x+ 2y= 29enters the window on the positivey-axisabove the other line, goes down and right, crosses the linex+ 2y= 19,and exits the window on the positivex-axis.
• The shaded region is above the two lines, right of they-axis,and above thex-axis.

Find both the maximum and minimum values of the function, if they exist, and the point at which each occurs. (If an answer does not exist, enter DNE.)The maximum value of the objective function is -------------- which occurs at

(x,y) = ---------

The minimum value of the objective function is--------- which occurs at

(x,y) =