Production Scheduling over Time A company has a permit to operate for five seasons. It can manufacture only during the first four seasons and in the fifth period it is only allowed to sell any leftover products. It can manufacture two types of products. One unit of product 1 requires five man-hours in preparatory shop and three man-hours in finishing shop. Each unit of product 2 requires six man-hours in preparatory shop and one man-hour in finishing shop. During each season the company has at most 12,000 man-hours in preparatory and 15,000 man-hours in the finishing shop (only during the first four seasons). The product manufactured during some season can be sold anytime from the next season onward. However, selling requires some marketing effort and it is expected that 10 and 20 minutes of premium radio marketing time (premium time occur during high volume listening hours) are required to sell 10 units of products 1 and 2 per period, respectively. Correspondingly, 25 and 40 minutes of non-premium radio marketing minutes are required to sell 10 units of products 1 and 2 per period, respectively. The costs of both premimum and non-premium radio marketing minutes are given in the table below. If a unit of product is available for sale during a season, but is not sold in that season, the manufacturer has to pay carryover charges of $10 per unit to put it up for sale again in the next season. The selling prices in the various seasons are given in the table below. How should the company operate in order to maximize the total profit?

Edit: I answered my own question below. Please comment with any feedback you have. Thank you.
 A: 
I don't know what to do with the "10 and 20 minutes of premium radio marketing time (premium time occur during high volume listening hours) are required to sell 10 units of products 1 and 2 per period, respectively. Correspondingly, 25 and 40 minutes of non-premium radio marketing minutes are required to sell 10 units of products 1 and 2 per period, respectively" part.

You have to express it as part of the 'cost of radio minutes' that you have written in the expression to be maximized.
10 minutes of premium radio marketing time are required to sell 10 units of product 1, incurring a cost of $10P_i$. Therefore, for one product, the cost incurred for advertising product 1 through premium radio is $P_i$. Similarly, 25 minutes of non-premium radio marketing time is required to sell 10 units of product 1, i.e. 2.5 minutes per product. Thus the total cost of advertising product 1 is $P_i + 2.5N_i$ per unit.
We can do the same thing for product 2.
A: $x_i=$ units of product 1 sold in season $i$
$y_i=$ units of product 2 sold in season $i$
$a_i=$ units of product 1 built in season $i$
$b_i=$ units of product 2 built in season $i$
$N_i=2.5x_i+4y_i$ (non-premium radio minutes in season $i$)
$P_i=x_i+2y_i$ (premium radio minutes in season $i$)
maximize $200x_2+450y_2+250x_3+400y_3+300x_4+400y_4+150x_5+300y_5-80P_2-20N_2-100P_3-40N_3-55P_4-10N_4-75P_5-25N_5-10(r_1+r_2+r_3+r_4+s_1+s_2+s_3+s_4-x_2+x_3+x_4+x_5+y_2+y_3+y_4+y_5)$
subject to
$5r_i+6s_i\leq 12000$
$3r_i+s_i\leq15000$
$N_2\leq 1000$
$P_2\leq200$
$N_3\leq 800$
$P_3\leq 400$
$N_4\leq 1000$
$P_4\leq200$
$N_5\leq 900$
$P_5\leq 300$
$x_i,y_i,r_i,s_i\geq 0$
