Maximizing Profits with Sandy Dandy Dune Buggies

Learn how to maximize profits with Sandy Dandy Dune Buggies by solving a mathematical problem involving the number of Crawlers and Rovers. Through steps such as identifying variables, creating a summary table, stating inequalities, graphing the feasible region, and substituting vertex coordinates, you can determine the best combination for a profit of $14,000.

• Maximizing Profits
• Mathematical Problem
• Sandy Dandy Dune Buggies
• Optimization
• Profit Maximization

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Uploaded on Oct 10, 2024 | 0 Views

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1. How Can I Find the Best Combination? Sec 5.2.3

2. Sandy Dandy Dune Buggies Read problem 5-87 on page 245. Write a full solution; see YOUR TASK on page 246. Include all the steps of the full solution as outlined.

3. Sandy Dandy Dune Buggies Step 1: Identify the variables: x is the number of the Crawlers y= is the number of the Rover

4. Sandy Dandy Dune Buggies Step 2: create a summary table to display all the given information: Parts Lamps Speak Employee hours ers 5 2 20 x y total 3 81 6 78 30 12*37.5=450

5. Sandy Dandy Dune Buggies Step 3: State all the inequalities: 1) ? 0 2) ? 0 3) ? 15 4) ? 12 5) 5? + 3? 81 6) 2? + 6? 78 12*37.5 7) 20? + 30? 450 ?????? ????: 500? + 1000?

6. Sandy Dandy Dune Buggies Step 4: Graph the feasible region and label all vertices: f(x)=12 f(x)=(81-5x)/3 f(x)=(78-2x)/6 f(x)=(450-20x)/30 x=15

7. Sandy Dandy Dune Buggies Step 4: the feasible region is below the graph below: f(x)=12 f(x)=(81-5x)/3 f(x)=(78-2x)/6 f(x)=(450-20x)/30 x=15; 0<y<2 vertices

8. Sandy Dandy Dune Buggies Step 4: the feasible region is below the graph below: f(x)=12 Shading 1 f(x)=(78-2x)/6 Shading 2 f(x)=(450-20x)/30 Shading 4 f(x)=(81-5x)/3 Shading 3 x=15; 0<y<2 vertices

9. Sandy Dandy Dune Buggies Step 5: substitute the coordinates of each vertex in the profit line to determine the maximum profit: 500(0) + 1000(12) = 12,000 500(3) + 1000(12) = 13,500 500(6) + 1000(11) = 14,000 500(12) + 1000(7) = 13,000 500(15) + 1000(2) = 9,500 500(15) + 1000(0) = 7,500 (6,11) produces the maximum profit of $14,000.

10. On your own: Review and Preview Page 247 #89-95 Review your notes. Rewrite and fortify them if needed. Update your vocab list, if needed.