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Optimizing Production for Maximum Profit - Sand Crab and Surf Mobile Strategy

Determine the ideal number of Sand Crabs and Surf Mobiles to produce per week for maximum profit. Calculate profit based on production constraints and vertex analysis. Graph the inequalities to find the optimal production quantity. Learn how to utilize resources efficiently for increased earnings.

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Optimizing Production for Maximum Profit - Sand Crab and Surf Mobile Strategy

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  1. Sand Crab and Surf Mobile Production

  2. Inequalities X represents number of Sand Crabs made. Y represents number of Surf Mobiles made. Maximum number of Sand Crabs that can be made per week: Maximum number of Surf Mobiles that can be made per week: Maximum number of manifold clamps per week: Maximum number of suspension joints per week: Maximum hours for production per week:

  3. X axis is sand crabs Y axis is surf mobiles Graph

  4. Vertices (0, 12) (3, 12) (6, 11) (12, 7) (15, 2) (15, 0) (0, 0) The vertices represent when all of the materials are used up, this is when you can have the maximum amount of profit.

  5. Profit Equation 500x+1000y= profit If you make 0 Sand Crabs and 12 Surf Mobiles you would makes $12,000 in profit. If you make 3 Sand Crabs and 12 Surf Mobiles you would have $13,500 in profit. If you make 6 Sand Crabs and 11 Surf Mobiles you would have $14,000 in profit. If you make 12 Sand Crabs and 7 Surf Mobiles you would have $13,000 in profit. If you make 15 Sand Crabs and 2 Surf Mobiles you would have $9,500 in profit. If you make 15 Sand crabs and 0 Surf Mobiles you would have $7,500 in profit. If you make 0 Sand Crabs and 0 Surf Mobiles you would have $0 in profit.

  6. Final Decision In order to make the most profit, you should make 6 sand crabs and 11 surf mobiles. You will earn $14,000. To figure this out, we needed to write seven inequalities and then graph them. By graphing them, we could figure out how to utilize all of the materials. If you use all the materials, then you can earn the most money. We tested the vertices by setting the inequalities equal to each other and solving.

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