Complements to S Programming by W.N.Venables and B.D.Ripley

By W.N.Venables and B.D.Ripley

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The only difference between the LP representation of the PPF and the neoclassical economic representation of the PPF is that the LP PPF does not result in a smooth and continuous frontier, whereas the neoclassical PPF is smooth and continuous. qxd 12/1/10 2:00 PM CHAPTER 1 Page 21 INTRODUCTORY CONCEPTS AND THE GRAPHICAL APPROACH TO LINEAR PROGRAMMING 21 In this example, it is assumed that the firm is a “price taker”: that is, the firm cannot influence the price it receives for x or y by varying production.

5 units. 33) which is exactly equal to the RHS value, and hence the third structural constraint is binding. The optimal (minimum) value of the objective function is: Z* ϭ 500x* ϩ 750y*, or Z* ϭ 500(50) ϩ 750(25) ϭ $43,750. qxd 12/1/10 2:00 PM CHAPTER 1 Page 31 INTRODUCTORY CONCEPTS AND THE GRAPHICAL APPROACH TO LINEAR PROGRAMMING 31 determined. In this case, Constraints 1 and 3 are binding. 38) In this case, the simultaneous equation method has verified that the graphical solution is indeed correct.

Step 2: Draw an iso-cost line. An iso-cost line is a set of solutions lying on a line whose objective function values are all the same. Similar to iso-contribution lines, all iso-cost lines are parallel to one another since their slopes are the same. Also, assuming that the objective function coefficients are positive, the value of iso-cost lines decreases as they move towards the origin. Step 3: Continue to move the iso-cost line towards the origin until a further movement makes all points lying on the iso-cost line infeasible.

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