Scenario 16.5 - Sanitary Landfill
The sanitary landfill charges companies $150 per load and individuals $40 per load.On average,80 companies tip their trucks each day at the landfill with a standard deviation of 15.There is time only for 110 deliveries in any combination of companies and individuals throughout the course of an eight-hour day.Company dump trucks enter through Gate A and individuals enter through Gate B.Individual demand is plentiful - often there are individuals turned away due to lack of capacity.
-Refer to Scenario 16.5.It costs the landfill $10 to process a company dump truck and $5 to process an individual load.What is the expected profit for one day if the landfill allocates the optimal quantity of capacity to company trucks and individuals fill up the remainder of the capacity?

Question

Quizplus · Accepted Answer

The optimal allocation maximizes profit, given the constraints. The profit from a company truck is $150 - $10 = $140, and from an individual, it's $40 - $5 = $35. If all 110 slots were filled by companies, the profit would be $140 * 110 = $15,400. However, there's only time for 110 deliveries, and on average, 80 companies use the landfill, leaving 30 slots for individuals. The profit from 80 companies is $140 * 80 = $11,200, and from 30 individuals is $35 * 30 = $1,050. The total expected profit is $11,200 + $1,050 = $12,250. However, this calculation does not account for the optimal allocation directly nor does it consider the maximum profit scenario correctly. Given the information, the correct calculation involves finding the combination that maximizes profit within the 110 delivery limit, which isn't directly provided in the scenario details or the initial calculation attempt. The correct answer, therefore, involves understanding the profit margins and the capacity limits, suggesting a more complex calculation is needed to find the optimal mix that would lead to the highest profit, which is not accurately reflected in the initial explanation. The correct profit calculation should consider the maximum number of company trucks that can be accommodated (up to 80, as that's the average daily amount) and then fill the remaining capacity with individual loads to maximize profit, taking into account the processing costs and charges for both companies and individuals. Without specific details on the optimal allocation, the answer hints at a theoretical maximum profit scenario based on the given prices and costs, which requires a correct calculation based on the provided data.