A company manufactures various electrical devices which are sold across the country.
We want to establish the manufacturing program for a certain device for the next 6
month. The sales department estimated that demand for the next 6 months
would be as follows:

The production department can manufacture this device on two shifts:
regular and additional. The maximum regular shift production rate is 20
units and 8 additional units on an additional shift for one day.
The production days are 21 days / month for each of the first 4 months. The
Last 2 months each have 20 production days.
Manufacturing costs are $ 20 per unit in regular shift and $ 35 per unit in shift
additional. The cost of storage, per unit per period (calculated on the stock at the end
period) is $ 15. The initial stock is 450 units and we want a final stock of
200 units at the end of the sixth month.
We want to formulate the linear programming model that would allow a
production scheduling at the lowest cost.
Note that, in order to meet the demands each month, the stock must be at the start
of one month plus the production during the same month must be greater than or equal to the
request this month.
Note also that the stock at the end of a month corresponds to the stock at the beginning of the month, plus the
production during the month, minus the demand for the month.
Answer questions a) to d) using the following variables:
X1 = number of units to be produced during month 1, in regular shift
Y1 = number of units to be produced during month 1, in additional shifts
X2 = number of units to be produced during month 2, in regular shift
Y2 = number of units to be produced in month 2, in additional shifts
X3 = number of units to be produced during month 3, in regular shift
Y3 = number of units to be produced in month 3, in additional shifts
X4 = number of units to be produced during month 4, in regular shift
Y4 = number of units to be produced in month 4, in additional shifts
X5 = number of units to be produced during month 5, in regular shift
Y5 = number of units to be produced in month 5, in additional shifts
X6 = number of units to be produced during month 6, in regular shift
Y6 = number of units to be produced during month 6, in additional shifts

questions:
a) Write the 6 constraints concerning the demand for each month.
b) Write the 12 constraints on the production capacities of each month.
c) Write the constraint on the stock at the end of the sixth month.
d) Write the economic function to be minimized.