Adding a form to a product drupal commerce
Your looking for product variations. Here are the official docs.


  Product attributes are the descriptors we use to define kinds of
  products. For example, we could describe a tshirt by the color and
  size. These attributes mean that in the real physical world your store
  may only carry one red shirt, but you have three sizes or three
  "variations." Commerce software must deal with product variations in a
  flexible way. Here's how Drupal Commerce abstracts it:
  
  Product Types. A product type is a specific bundle based on a custom
  product entity. Each bundle can have fields attached to it, including
  pictures and other kinds of information.&lt;
  
  Product "Informational"
  Fields. Any field on a product can be a simple "informational" field.
  Typical informational fields include an image of that specific
  configuration of a product. For example, if you sell a tshirt with a
  cool print in multiple colors, each product with a different color
  could have an image field that, when displayed on the product display
  node, will change when you select different attributes (like color).
  
  Product "Attribute" Fields. Any field on a product type with a defined
  list of options (list of text options, list of taxonomy terms, list of
  colors). The attribute fields are special because of the way they turn
  into selection widgets on a product display. Often you will pair an
  attribute field (like a color dropdown) with an information field
  (like an image field) to let the user "select" the blue tshirt and the
  Drupal Commerce system will quickly load the picture associated with
  the blue product.
  
  Product Displays. If needed at all, these are
  groupings of products. You can reference any type and number of
  products on a product display. In order to make use of product
  displays, we recommend only showing one type of product per product
  display. The product display is where you typically see the product
  with drop downs to "configure" or "order" the right kind of product.


For the different pricing of the variations refeer here: Automatic product variations pricing.