Determining the cost strategy for manufacturing pipes

Question

Assignment:

A materials supply plant in Cypress, TX produces concrete pipe products. The plant is scheduling production of a certain size concrete sewer pipes over the next 5 months. Any pipe on hand at the beginning of the first month has been subtracted from the first month's requirement. The manager wants to meet the projected demand over the 5 months period at minimum cost. Constraints are imposed on the monthly regular rate processing time and the amount of raw material available each month.

The table below gives cost and availability data for the problem at hand. It take 75 hours. of processing time to produce one unit of sewer pipe and it costs approximately $40 to store one unit of pipe for 1 month. If it is assumed that no pipe will be carried over after the fifth month, construct the I.P model for determining the minimum cost strategy ($) for manufacturing the pipes, using the following variable definitions:

XR_i = units of pipe produced during month L on regular time

XO_i, units of pipe produced during month L on overtime

XS_i = units of pipe stored from month I to month i + 1