Vivian's Gem Company produces two types of gems: Types 1 and 2. Each Type 1 gem contains 2 rubies and 4 diamonds. A Type

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Vivian S Gem Company Produces Two Types Of Gems Types 1 And 2 Each Type 1 Gem Contains 2 Rubies And 4 Diamonds A Type 1 (227.33 KiB) Viewed 33 times

Vivian's Gem Company produces two types of gems: Types 1 and 2. Each Type 1 gem contains 2 rubies and 4 diamonds. A Type 1 gem sells for $10 and costs $5 to produce. Each Type 2 gem contains 1 ruby and 1 diamond. A Type 2 gem sells for $6 and costs $4 to produce. A total of 30 rubies and 50 diamonds are available. All gems that are produced can be sold, but marketing considerations dictate that at least 11 Type 1 gems be produced. Let x1 = number of Type 1 gems produced and x2 = number of Type 2 gems produced. Assume that Vivian wants to maximize profit. Use the LINDO printout below to answer the following questions: A. What would Vivian s profit be if 35 rubies were available? B. A vendor offers to sell 2 diamonds at a cost of $1 above current prices. What would Vivian s new profit be given Vivian accepts the offer? C. If type 1 gems sold for only $15, what would be the new optimal solution to the problem? D. What would Vivian s profit be if 46 diamonds were available? LINDO Output for Vivian's Gem MAX SUBJECT TO 2) 3) 4) END VARIABLE LP OPTIMUM FOUND AT STEP X1 X2 ROW 2) 3) 4) 5 X1 + 2 X2 2 X1 + 4 X1 + X1 NO. ITERATIONS= X1 X2 ROW OBJECTIVE FUNCTION VALUE 1) 67.0000000 VALUE 11.000000 6.000000 SLACK OR SURPLUS 2.000000 .000000 .000000 X2 <= 30 X2 <= 50 11 VARIABLE CURRENT COEF 5.000000 2.000000 RANGES IN WHICH THE BASIS IS UNCHANGED: 2 CURRENT RHS 30.000000 2 3 50.000000 4 11.000000 REDUCED COST .000000 .000000 OBJ COEFFICIENT RANGES ALLOWABLE INCREASE 2 DUAL PRICES 0.000000 2.000000 -3.000000 3.000000 INFINITY RIGHTHAND SIDE RANGES ALLOWABLE INCREASE INFINITY 2.000000 1.500000 ALLOWABLE DECREASE INFINITY .750000 ALLOWABLE DECREASE 2.000000 6.000000 1.000000