fixed an marginal cost calculation issue I'm trying to solve a question that is quite difficult for me. I did part of the question but, bit difficult to decide the exact answer for the below question. 

After coming up with an innovative idea for a new product, you paid 4000 
to an industrial designer to draw the blueprints and found a factory in China that agreed to produce the product for you for $3 per unit (the price includes the shipping cost from China to you). 

Since this is a totally new and unique product, you have no idea how the demand for it would be. Therefore, before you start pricing the product and ordering large amounts from the Chinese factory, you decide to run an experiment (or a pilot study): you talk to Target and they allow you to sell your product at 11 different Target stores for 11 different prices (a different price at each store). These stores are located in areas whose residents have similar average income, so you can be certain that price (and not income) is the only factor varying among these stores. 

After 2 weeks, Target sends you the sale numbers for your product.

Price   Quantity Demanded
4   221
5   210
6   185
7   162
8   144
9   122
10  102
11  81
12  61
13  46
14  25


What they are asking is to measure the total fixed cost and the marginal cost. 

Can 4000 be decided as the fixed cost? If so how the marginal cost can be calculated? I believe the variable cost is 3$. This 4000 should be only the initial fixed cost. How can I calculate the marginal cost.
The marginal cost is 3. Marginal costs do not depend on the fixed cost, and when your variable costs are constant, then the marginal cost and the variable cost are the same. Note that your total cost is $C=FC+3q$ and the marginal cost is always the derivative of your total cost, in this case, $3$.

As for the fixed costs, 4000 is definitely part of it, but maybe also the forgone profits from selling the goods in the various stores at sub-optimal prices, as pointed out by another response. Other's have pointed out that if you calculate the variable profits for each price, 9 gives the largest profits, so in all the other stores that you made less profits, the lost profits should probably be added to the fixed cost.