# Thread: linear programming question solver excel

1. ## linear programming question solver excel

Hi, i'm having hard time solving this probem:
" This is a multiperiod production problem scheduling problem. Plastic Molding manufacturer is planning the production storage and marketing of a product whose demand and selling price vary seasonally.The company is in the process of developing a manufacturing strategy. According to the formulated strategy, the company wants to manufcature the product in the seasons during which production costs are low, and then store and sell product when selling price is high. The manufacturer has obtained the following estimates of the demand, cost, capacity, and expected selling price of the product for each period.
Let Pj = Product made (in tons) during period j.
Ij= product left in storage at the end of period j
Dj= product demanded during period j
Beginning inventory = 500 tons
Desired ending inventory = 300 tons
(inventory ) storage cost = \$2 per ton form one period to the next

Period ----Production cost ----Production capacity---- Demand---- Price
1 ---------20------------------ 1500---------------------1100 -------180
2 ---------25------------------ 2000--------------------- 1500 -------180
3 ---------30 ------------------2200 --------------------1800 --------250
4 --------40------------------- 3000 --------------------1600 --------270
5 -------50 --------------------2700 --------------------2300 --------300
6 -------60 --------------------2500-------------------- 2500 --------320

Formulate the linear programming problem that provides the optimal production schedule and maximizes the total profit

And also the second problem:

BH Canada designs and manufacturers high-grade palstic based products for industrial, commercial, and residential use. The company is considering leasing a local warehouse to fullfill its needs for aditional storage spaces over the next 4 months

Month --Additional storage space
1 -------5000
2 -------3500
3 -------6500
4 -------4000

A local warehouse company has offered short term leasing options that differ in terms of the length of lease

Option ---Length of lease--- Cost per square metre
1 ---------1 month ----------1.50
2--------- 2 months ---------2.10
3 ---------3 months--------- 2.85
4--------- 4 months ----------3.40

Given that the monthly reguirements for additional storage spaces are variable, the company considering acquiring lease options that differ in terms of length and space size at the beginning of each month
Formulate a linear programming model that can be used by the company to determine the minimum cost for additional storage space

2. here' s what i got for the second problem
Objective function:
1.50 x11+1.50 x21 +1.50x31+1.50x41+2.10x12+2.10x22+2.10x32+2.10x42+2 .85x13+2.85x23 +2.85x33+2.85x43 + 3.4x14+3.4x24+3.4x34+3.4x44
Constraints:
X11=5000
X12=5000+3500
X13= 5000+3500
X14= 5000+3500+4000
X21=3500
X22=3500+6500
X23=3500+6500+4000
X24=0

X31=6500
X32=6500+4000
X33=0
X34=0

X41=4000
X42=0
X43=0
X44=0

X24, x33, x34, x42, x43, x44 = 0

3. I'm stuck on the same question. Can any 1 help me with the second question? I don't even get what the question is asking. Please help