The Meredith Ribbon Company produces paper and fabric decora

The Meredith Ribbon Company produces paper and fabric decorative ribbon which it sells to paper products companies and craft stores. The demand for ribbon is seasonal. Information about projected demand and production for a particular type of ribbon is given.

Demand (yards)

Production Cost Per Yard

Production Capacity (yards)

Quarter 1

10,000

.03

30,000

Quarter 2

18,000

.04

20,000

Quarter 3

16,000

.06

20,000

Quarter 4

30,000

.08

15,000

An inventory holding cost of $.005 is levied on every yard of ribbon carried over from one quarter to the next.

a.

Define the decision variables needed to model this problem.

b.

The objective is to minimize total cost, the sum of production and inventory holding cost. Give the objection function.

c.

Write the production capacity constraints.

d.

Write the constraints that balance inventory, production, and demand for each quarter. Assume there is no beginning inventory in quarter 1.

e.

Solve for the value of minimum objective function. Provide copy of the solution spreadsheet.

Solution