Question $4.$ Anderson currently produces and sells $1,260$ tons of Y$48$ per month, with average production runs of $36$ tons and average shipments of $2$ tons. The production manager has recently discovered a different kind of raw material which if used would significantly improve the quality of Y$48.$ However production costs would be higher. Specifically, the raw material cost per ton of finished Y$48$ would increase by $$120,$ and quality control costs would increase by $$6,000$ per production run. The marketing manager believes that many of Anderson$$s customers would pay a higher price of $$3,100$ per ton if the higher quality Y$48$ is offered, but Anderson would also lose a significant number of its customers to competitors who offer lower quality substitutes at lower prices. The marketing manager also believes that at the higher price of $$3,100$ per ton, a greater sales effort will be required, increasing the fixed marketing expense by $$36,960$ per month. Overall, the marketing manager believes that the high quality, high price strategy is a gamble because he is uncertain about the quantity that would be demanded if this strategy is adopted. Assuming that the average size of production runs and shipments would remain unchanged, how many tons of the higher quality Y$48$ would need to be sold $($and shipped$)$ at the contemplated price of $$3,100$ in order to maintain the monthly profits of Anderson at its current level?

Hint: Work in terms of production runs and then convert production runs into production tons.