Mills Corp. produces memory enhancement kits for game systems. Sales have been very erratic, with some months showing a loss. The company's contribution format income statement for the most recent month is below:

Sales $(25,000$ units at $$40$ per unit$)$ $$1,000,000$

Variable expenses $500,000$

Contribution margin $500,000$

Fixed expenses $600,000$

Net operating loss $ $(100,000)$

Required:

a$)$ Compute the company's break$-$even point in both units and dollars.

b$)$ The sales manager feels that a $$100,000$ increase in the monthly advertising budget, combined with an intensified effort by the sales staff, will result in a $$300,000$ increase in monthly sales. If the sales manager is right, what will be the effect on the company's monthly net operating income or loss?

c$)$ Refer to the original data. The president is convinced that a $10\%$ reduction in the selling price, combined with an increase of $$100,000$ in the monthly advertising budget, will cause unit sales to double. What will the new contribution format income statement look like if these changes are adopted?

d$)$ Refer to the original data. The company's advertising agency thinks that a new package would help sales. The new package proposal would increase packaging costs by $$2\mathrm{.}00$ per unit. Assuming no other changes, how many units would have to be sold each month to earn an after$-$tax profit of $$30,000?$ Mills has a tax rate of $20\%.$