Page 92 : Carla's Maps

(1) The production quantities of maps A, B, C and D respectively are 1500, 1000, 1000 and 2833.33. The projected profit is 10166.66.

(2) Carla would be willing to pay 0.5, 0 and 0.166 (shadow prices of constraints) dollars for extra units of prinitng, cutting and folding time respectively. The number of extra hours for which Carla would be willing to pay these prices are 1000, and 7000 (allowable increases of respective constraints).

(3) Maps B and C have negative shadow prices; hence production of these would be decreased and the savings resulting from a reduction of 100 units for either of these would result in a savings of -100(-0.33) = 33.33.

(4) The least amount of profit required for considering production of the fifth map would be 2(0.5)+0+3(0.166) = 1.5 dollars per map. Further analysis is required to see the effect of requiring 1000 of these.

(5) It is known that the profit for D is in the range (2-0.25,2+0.25) = (1.75,2.25). The sensitivity report tells us that the allowable decrease and increase in the objective coefficient for D are 0.5 and 1 respectively; i.e., the solution will not cvhange as long as the profit per map is in the range (2-0.5,2+1) = (1.5,3). Since the former range is a subset of the latter further analysis is not worth the extra cost.