Can you make detailed handwritten solution , GAMS programming solution and interpret the results.

5. [20 points) A company sells four types of boxes (B1,...,B4), ranging in size from 24 to 33 cubic feet (size is measured as volume). The demand and size of each box is given in the table below. The variable cost (in dollars) of producing each box is equal to the box's volume. A fixed cost of $1,000 is incurred to produce any of a particular box. If the company desires, demand for a box may be satisfied by a box of larger size. Formulate and solve a shortest-path problem whose solution will minimize the cost of meeting the demand for boxes. B1 B2 B3 B4 Size 33 30 Demand 400 300 26 500 24 700 Considering that this problem can be formulated as a shortest path model, answer the following questions: (a) (10 points] Define nodes, arcs, and arc properties in words. Calculate all arc costs and show your calculations in detail. Draw the network graph showing the relevant parameter values on the network. (b) [10 points] Formulate the shortest-path model for this problem. (Reminder: Generic formulations will not receive any points.)