4) min 4x1 + 3x2 + 6x3 s. t. x1 + 0.5x2 + x3 ≥ 15 2x2 + x3 ≥ 30 x1 + x2 + 2x3 ≥ 15 x1,x2,x3 ≥ 0 a) find the optimal solution by entering this problem into excel. b) run the sensitivity report and use it to find the optimal solution to the dual problem [do not solve the dual by using solver]. c) formulate the dual problem. d) verify that the strong duality theorem and all complementary slackness conditions (there are six of them) hold.

10 glasses of juice could be made with 5 carrots, 1,500 orange juice, 2,000 papaya juice.

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

step-by-step explanation: