Chalmers Corporation operates in multiple areas of the globe, and relatively large price changes are common. Presently, the company sells $105,600$ units for $$50$ per unit. The variable production costs are $$20,$ and fixed costs amount to $$2,079,000.$ Production engineers have advised management that they expect unit labor costs to rise by $10$ percent and unit materials costs to rise by $15$ percent in the coming year. Of the $$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 yean

Required:

a$.$ 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.

b$.$ 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.

c$.$ If the volume of sales were to remain at $105,600$ units, calculate the new price that would be required to attain the $8$ percent increase in profits.

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