Question

A plant assembles chairs and tables. The average assembly times are 20 minutes/chair. Sales

forecasts for the next three months are given in the table.

Product March April Current inventory

Chair 2800 2300 30

Table 500 800 100

The production costs and the selling prices for the products are shown next.

Product Unit cost Unit price

Chair $150/chair $250/chair

table $400/table $750/table

Monthly inventory charges are 2% of the production cost.

The workforce will be available up to 32000 hours / month

3. a) Please formulate above scenario as LP for minimizing the total production costs.

First, define your decision variables, and then use them in your LP model.

3. b) Please solve the LP model you created on

define your decision variables, then objective function and constraints.

Answer 1

a) LP model is as follows

Let C1, C2 and T1, T2 be the number of Chairs and Tables to produce in month of March and April respectively

VC and VT be the inventory of Chairs and Tables in March

Objective: Max (250-150)*(C1+C2)+(750-400)*(T1+T2)-150*2%*VC-400*2%*VT

s.t.

(20/60)*(C1+T1) <= 32000

(20/60)*(C2+T2) <= 32000

C1-VC = 2800-30

C2+VC = 2300

T1-VT = 500-100

T2+VT = 800

All variables >= 0

b) Solution of LP model is following

Solution:

Chairs to be produced in March (C1) = 2770

Chairs to be produced in March (C2) = 2300

Tables to be produced in March (T1) = 400

Tables to be produced in March (T2) = 800

Optimal value = $ 807,000