HW_Solution_Chapter 06_EMSE102-202

HW_Solution_Chapter 06_EMSE102-202 - OR CHAPTER 6 SOLUTIONS...

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1 OR CHAPTER 6 SOLUTIONS SECTION 6.1 5. 5a. Let c1 = profit from type 1 radio. Slope of isoprofit line is -c1/2. Current basis is still optimal if of isoprofit line is steeper than L1 constraint and flatter than L2 constraint or-2 -c1/2 -.5 or 1 c1 4 or $23 = 22 + 1 Type 1 price 22 + 4 = $26. 5b. Current basis remains optimal for -2 -3/c2 -.5 or 1.5 c2 6 or $21.50 Type 2 price 26. 5c.Optimal solution still occurs where both constraints are binding or x 1 + 2x 2 = 30 and 2x 1 + x 2 = 50. This yields x 1 = 70/3, x 2 = 10/3, and z = 230/3. Since solution is feasible, it is optimal. 5d. Optimal solution occurs where x 1 + 2x 2 = 40 and 2x 1 + x 2 = 60. This yields x 1 = 80/3, x 2 = 20/3, z = 280/3.
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2 5e. If 40 + laborer 1 hour are available optimal solution is where x 1 + 2x 2 = 40 + and 2x 1 + x 2 = 50. This yields x 1 = 20 - /3, x 2 = 10 + 2 /3, z = 80 + /3. Thus laborer 1 shadow price = 1/3. If 50 + laborer 2 hours are available optimal solution is where x 1 + 2x 2 = 40 and 2x 1 + x 2 = 50 + . This yields x 1 = 20 + /3, x 2 = 10 - /3, z = 80 + 4 /3. Thus laborer 2 shadow price = 4/3.
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