For the fiscal year that ends on December $31,2023,$ Acme Model Ltd$.$ is planning about its sales budget. Below are the necessary information for the year that concluded on December $31,2022$:

Units sold $23000$

Selling price $30$ per unit

Variable costs $20$ per unit

Fixed costs $180000$

They are evaluating three different strategies. It is anticipated that the variable costs per unit in each scenario will stay the same.

Plan $1$

To increase demand, lower the selling price by $8\%.$

Plan $2$

Raise the selling price by $8\%$ so that the increased revenue surpasses the loss in sales

Plan $3$

Maintain the sale price at $30.$ The basic income of sales employees would be lowered, and they would instead receive a modest base pay plus a commission rate of $4$ for each item they sell. By doing this, the fixed costs would drop by $70,000.$

Required:

i$)$ Determine the break$-$even point in units as well as the profit for the fiscal year that ended on December $31,2022.$

ii$)$ Determine the unit sales needed to satisfy the requirements of Plans $1,2,$ and $3$ in order to keep the profit level for the year that ended on December $31,2022.$

iii$)$ Determine what would happen if plan $3$ were implemented, then compare it to the break$-$even point for the year that concluded on December $31,2022.$

Workings are required