RedEx Transport's Rail Division has an annual capacity to process 800,000 tons of gravel used as a base under railroad tracks by railroads. The normal selling price is $62 per ton. At current operating levels, fixed costs are $10 per ton and variable costs are $32 per ton. The Air Division of RedEx Transport would like to buy 200,000 tons of gravel from the Rail Division to use in producing quality aggregate to be used for runways. The Rail Division is operating at 100 percent of capacity. The Air Division currently buys the gravel for $55 per ton from an outside source. The Rail Division can save $5 per ton in variable costs on the transfer. What is the lowest price the Rail Division should consider if it wishes to see no decline in profits?

Question

Quizplus · Accepted Answer

The Rail Division's current profit per ton sold is the selling price of $62 minus the total variable and fixed cost per ton, which is $10 + $32 = $42.

If the Rail Division sells 200,000 tons of gravel to the Air Division, it will save $5 per ton in variable costs, reducing their total variable cost per ton to $27. The Rail Division's profit per ton sold to the Air Division would be the selling price of $55 (the Air Division's current price) minus the total variable and fixed cost per ton, which is $10 + $27 = $37.

To maintain the same profit per ton, the Rail Division needs to sell the gravel to the Air Division for $62 - $37 = $25 per ton more than their variable cost per ton. Therefore, the lowest price the Rail Division should consider while still maintaining their profits is:

$27 + $25 = $52 per ton.

Since this price is higher than the Air Division's current price of $55 per ton, the Rail Division should sell the gravel to the Air Division for $55 per ton.

RedEx Transport's Rail Division Has an Annual Capacity to Process