A company offers two versions of its main products: basic and luxury. The manufacturing process for these products is capital$-$intensive $($i$.$e$.$ primarily relies on the use of machines$).$ The unit contribution margins for basic and luxury are $$155\mathrm{.}40$ and $$121\mathrm{.}80$ respectively. The company has $310$ uncommitted hours of machine time that can be allocated to manufacturing more products. The machine hours used to produce one unit of basic is $2.$ The machine hours used per unit of luxury is $3.$

Do not enter dollar signs or commas in the input boxes.

Round your answers to $2$ decimal places.

a$)$ Calculate the contribution margin per machine hour for each product.

Basic: $

Luxury: $9$

b$)$ Which product, basic or luxury, should be produced using the uncommitted machine hours? Assume that there are no capacity constraints.

Item to be produced:

c$)$ How many units of the product selected in part b$)$ above will be produced using the uncommitted machine time?

Round the number of units to $2$ decimal places.

Number of units:

d$)$ What is the company's increase in contribution margin if the product selected in part b$)$ will be produced using the uncommitted machine time? Increase in contribution margin: $