$[20$ points$]$ Ray Holt seeks investment for his new business. The investor will bear all the costs $($fixed $+$ variable$)$ and requests a rate of return of at least $y\%.$ For the business fixed cost is $F_c,$ selling price of a unit is $S_p,$ and Cost of production of a unit is $C_p.$ How many units, $x,$ should Ray Holt make to meet the investor's rate of return requirement?

a$.$ Develop a model to calculate the number of units required to produce $(x)$ using the variables and parameters. $($y$,$ Fc$,$ Sp$,$ Cp$)$

b$.$ Using the above model, calculate the number of units required to produce if the requested rate of return is $12\%,$ fixed cost is $$15,000,$ selling price is $$15,$ and cost of production is $$7.$