CVP analysis with Sales Mix

Manzeck Bicycles International produces and sells three different types of mountain bikes. The sales mix, expressed as a function of total units sold, is as follows. The company's total fixed costs to produce the bicycles are $$7,500,000.$ Information regarding the three models is shown below.

$\backslash$table$[[,$Pro,Intermediate,Standard,Total$],[$Units sold,$5,000,10,000,25,000,40,000],[$Selling price,$$800,$$$500,$$$350,],[$Variable costs,$$500,$$$300,$$$250,]]$

$($a$)$ Determine the number of units of each model that the company must sell to break even.

$($b$)$ Determine the number of units of each model that the company must sell to make a target profit of $$1,500,000$ under this product mix.