In response to a growing awareness of gluten allergies, Sheridan Bakery tried using gluten$-$free flour in its three most popular cookies. After several attempts and a lot of inedible cookies, the company perfected new recipes that yield delicious gluten$-$free cookies. The costs of producing a batch of $100$ cookies are as follows:

Chocolate

Chip Sugar Oatmeal

Raisin

Sales price $$130$ $$118$ $$125$

Variable cost $$75$ $$69$ $$72$

Fixed cost $161521$

Total cost $918493$

Gross profit $$39$ $$34$ $$32$

Pounds of flour $2\mathrm{.}52\mathrm{.}52$

a$.$ Assuming no raw material constraints and unlimited demand for cookies, calculate contribution margin per batch for Chocolate Chip, Sugar, Oatmeal Raisin cookies.

b$.$What type of cookies would maximize the company's contribution margin?

c$.$Assume thaataa, based on typical customer demand, carla vista will sell $11,600$ batches of chocolate chips cookies, $7600$ bathces of sugar cookies $,$ and $9,600$ batches of oatmeal rasin cookies $.$ what would the company's contribution margin be$?$

d$.$ Carla vista's flour supplier has announced a shortaaage of gluten free flour. As a as a result, Carla Vista will only be able to purchase $48,200$ pounds of flour

How many batches of each type of cookie should the company bake?

What will the companies contribution margin be$?$