A company is planning a new product. Market research information suggests that the new product will sell $10,000$ total units at a price of $$21\mathrm{.}00$ per unit. The company estimates the lifetime costs of the product as follows:

$\backslash$table$[[$Estimated costs$],[$Design and development costs:,$$50,000,],[$Manufacturing costs:,$$10\mathrm{.}00,$per unit$],[$End$-$of$-$life costs:,$$20,000,]]$

The company estimates that if it were to spend an additional $$15,000$ on design, then manufacturing costs could be reduced.

a$)$ What is the target cost of the product if the company seeks a markup of $40\%$ of product

Round answer to two decimal places. $

Given the target cost, would you expect the company to launch the product What is the maximum allowable product manufacturing cost per unit if the markup of $40\%$ of the original life$-$cycle cost?

Round answer to two decimal places.

Using the total life$-$cycle cost to determine target product cost, would you expect the company to launch the product?

c$)$ Assume the additional $$15,000$ was spent on design. By how much would the design changes need to reduce the per unit product cost to meet the goal of a $40\%$ markup on total life$-$cycle costs?

Round answer to two decimal places. $