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 graphical sensitivity analysis to answer the following questions: (a) What would Vivian’s profit be if 46 diamonds were available? (b) If Type 2 gems sold for only $5.50, what would be the new optimal solution to the problem? (c) What would Vivian’s profit be if at least 12 Type 1 gems had to be produced?
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 graphical sensitivity analysis to answer the following questions:
(a) What would Vivian’s profit be if 46 diamonds were available?
(b) If Type 2 gems sold for only $5.50, what would be the new optimal solution to the problem? (c) What would Vivian’s profit be if at least 12 Type 1 gems had to be produced?
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