During $2024,$ Vertex Industries sold $75,000$ units of its only product for $$32$ per unit. Manufacturing and selling the product required $$140,000$ of fixed manufacturing costs and $$240,000$ of fixed selling and administrative costs. Its per unit variable costs were as follows: Materials $$10\mathrm{.}00$ Direct labour $$5\mathrm{.}00$ Variable overheads $$2\mathrm{.}00$ Variable selling & administrative expenses $$1\mathrm{.}00$ In the current year $2025,$ the company will use new material that is easier to work with. The new material will reduce material costs by $30\%$ and direct labour costs by $40\%$ and will not affect quality or marketability. Management is considering an increase in the unit sales price to reduce the number of units sold because the factory$$s output is nearing its annual capacity of $80,000$ units. Two plans are being considered: Plan A$-$ the company will keep the selling price at the current level and sell the same volume as last year. Plan B$-$ the company will increase selling price by $25\%.$ This price will decrease unit sales volume by $10\%.$ Under both plans, fixed selling and administrative costs and all variable costs per unit will remain the same. However, under plan B$,$ fixed manufacturing cost will increase by $$25,000.$ Required: $1.$ Determine the break$-$even points under Plan A and Plan B $(4$ marks$)2.$ Determine the net income under Plan A and Plan B $(20$ marks$)3.$ Using Excel, prepare a fully labelled breakeven chart for both plan A and plan B$.$ Charts should display all major and minor gridlines. $(20$ marks$)4.$ Advise the company, based on your results whether it should choose plan A or B$.(6$ marks$)$