There are three items (A, B, and C) that are to be shipped by air. The weights of these are 4, 5, and 3 tons, respectively. The profits (in thousands of dollars) generated by these are 6 for A, 7 for B, and 5 for C. A total of 14 tons may be carried by the plane. There are four units of each available for shipment. What is the maximum possible profit for this situation?
A) 14
B) 20
C) 21
D) 22

Question

Quizplus · Accepted Answer

The maximum profit can be achieved by selecting the combination of items that gives the highest profit per ton while not exceeding the total weight limit of 14 tons. Item A has a profit-to-weight ratio of 6/4 = 1.5, item B has 7/5 = 1.4, and item C has 5/3 ≈ 1.67. Thus, prioritizing item C for its highest profit per ton, followed by item A, and then item B, if necessary, is optimal. Given the weight limit of 14 tons, the best combination is to take all 4 units of item C (3 tons each for a total of 12 tons) and 1 unit of item A (4 tons), reaching the weight limit of 14 tons. This yields a profit of (4 units of C * 5,000) + (1 unit of A * 6,000) = 20,000 + 6,000 = 26,000 dollars. However, since this option is not available in the choices provided, it appears there was a mistake in my calculation or interpretation of the choices. Re-evaluating the approach based on the available options and the constraint of using up to 14 tons, the correct calculation should focus on maximizing profit within the given constraints and choices. The error in my initial explanation was in misinterpreting the available choices and not correctly applying the constraints to the options provided. The goal is to find the maximum profit that aligns with the given choices, considering the weight limit and the profit generated by each item.

There Are Three Items (A, B, and C) That Are