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Levart [38]
3 years ago
11

Consider the following five constraints x1 + 2x2 ≤ 3, x1 − x2 ≥ 0, 2x1 + x2 ≤ 3, x1 + 5x2 ≤ 6, x1 − 2x2 ≥ −1. (a) Sketch the fea

sible region and find the degenerate vertex x0. (b) How many possible working sets are there at x0? (c) Suppose that we wish to minimize x1 + x2 subject to these constraints, starting at x0 and using the simplex method. Find a working set A0 for which the Lagrange multiplier vector λ (the solution of AT 0 λ = c) contains at least one negative component λs, but the simplex search direction satisfying A0p = es is not a feasible descent direction. Draw a picture showing p emanating from x0. What are the blocking constraints? (d) Under the same conditions as in part (c), find a working set A¯ 0 for which the Lagrange multiplier vector contains at least one negative component, but the associated search direction ¯p is a feasible descent direction. Draw a picture showing ¯p emanating from x0. (e) Can you find a feasible descent direction at x0 if we wish instead to minimize −x1 − x2? Explain your answer.
Business
1 answer:
chubhunter [2.5K]3 years ago
6 0

Answer:

Answer for the question:

Consider the following five constraints x1 + 2x2 ≤ 3, x1 − x2 ≥ 0, 2x1 + x2 ≤ 3, x1 + 5x2 ≤ 6, x1 − 2x2 ≥ −1. (a) Sketch the feasible region and find the degenerate vertex x0. (b) How many possible working sets are there at x0? (c) Suppose that we wish to minimize x1 + x2 subject to these constraints, starting at x0 and using the simplex method. Find a working set A0 for which the Lagrange multiplier vector λ (the solution of AT 0 λ = c) contains at least one negative component λs, but the simplex search direction satisfying A0p = es is not a feasible descent direction. Draw a picture showing p emanating from x0. What are the blocking constraints? (d) Under the same conditions as in part (c), find a working set A¯ 0 for which the Lagrange multiplier vector contains at least one negative component, but the associated search direction ¯p is a feasible descent direction. Draw a picture showing ¯p emanating from x0. (e) Can you find a feasible descent direction at x0 if we wish instead to minimize −x1 − x2? Explain your answer.

is given in the attachment.

Explanation:

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Answer:

Dollar profit loss = $3

Holding period return = negative 9%

Explanation:

In order to find the dollar profit or loss return we will add the dividend and selling price because that the dividend plus the selling price is the cash that Travis receives or the positive cash and we will subtract the buying price from it because it is the negative cash flow. So we will add all the positive cash flows and subtract negative cash flow from it in order to find the dollar profit loss or return.

Selling price = 27.65

Dividend = 0.85

Selling price + Dividend= 28.5

Selling price = 31.50

Dollar profit loss or return = 28.50-31.5=-3

Loss= $3

In order to find the holding period return we will divide add the dividend and selling price , subtract buying price from it and then divide it by buying price.

(27.65+0.85-31.5)/31.5= -0.09 = -9%

Holding period return = negative 9%

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Santorino Company produces two models of a component, Model K-3 and Model P-4. The unit contribution margin for Model K-3 is $6;
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