AMS 341Spring, 2010Homework Set # 5 — Solution Notes#5, 5.1:a45a54x210Cx110ADB(20,10)(a) The slopes are-12for the first constraint and-2 for the second. To keep the current basis remain optimal, theslope-c12of the isoprofit line must satisfy-2≤ -c12≤ -12. Thus, the profit from type 1 radioc1satisfies 1≤c1≤4.The profit is equal to the price minus the cost of producing one type 1 radio, which is 22. The price of type 1 radio isbetween $23 and $26.(b) Similar to (a), suppose the profit from type 1 radio is fixed, and the profit from type 2 radio isc2the isoprofit linemust satisfy-2≤ -3c2≤ -12. and therefore 1.5≤c2≤6. The price of type 2 radio is between $21.5 and $26.(c) At point C, we havex1+ 2x2= 25. As long as laborer 1 work no less than 25 hours per week, the current basiswill remain optimal. Therefore, in this problem the basis is still optimal and the new optimal solution isz=2303,x1=703,x2=103.
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Equals sign, optimal solution, The Shadow, Shadow price, current basis