Chalmers Corporation operates in multiple areas of the globe, and relatively large price changes are common. Presently, the company sells $165,400$ units for $$50$ per unit. The variable production costs are $$20,$ and fixed costs amount to $$2,085,500.$ Production engineers have advised management that they expect unit labor costs to rise by $10$ percent and unit materials costs to rise by $15$ percent in the coming year. Of the $$20$ variable costs, $25$ percent are from labor and $50$ percent are from materials. Variable overhead costs are expected to increase by $20$ percent. Sales prices cannot increase more than $12$ percent. It is also expected that fixed costs will rise by $10$ percent as a result of increased taxes and other miscellaneous fixed charges.

The company wishes to maintain the same level of profit in real dollar terms. It is expected that to accomplish this objective, profits must increase by $8$ percent during the year.

Required:

Compute the volume in units and the dollar sales level necessary to maintain the present profit level, assuming that the maximum price increase is implemented.

Compute the volume of sales and the dollar sales level necessary to provide the $8$ percent increase in profits, assuming that the maximum price increase is implemented.

If the volume of sales were to remain at $165,400$ units, calculate the new price that would be required to attain the $8$ percent increase in profits? Calculate the new price.