EXECUTIVE SUMMARY
Shelby Shelving is a small company that produces two types of shelves for stores (Model S and Model
LX). Shelves are manufactured in three steps: stamping, forming and assembly. In the stamping stage, a
large machine is used to stamp standart sheets of metal into appropriate sizes. In the forming stage,
another machine bends the metal into shape. Assembly involves joining the parts with a combination of
soldering and riveting.
Although the shelves are selling well, the total profit of the company is a concern. An engineer suggested
that the current production of model S should be cut back because Model S shelves are sold for $1800
per unit but their costs are $1839. Therefore, company is losing money on each one. But the controller
disagreed with that idea. He thought that the problem was the model S assembly department trying to
absorb a large overhead with a small production volume.
Our aim is to determine the optimal monthly production in order to maximize the total profit while
satisfying the resource constraints such as assembly capacity and available hours for stamping and
forming. We will use Excel Solver for optimizing monthly production and for maximizing total profit.
MODEL
We have to determine monthly production of Model S and LX and therefore we have to maximize the
total profit. But there are some limitations of company and also there are some assumptions.
Assumptions
-
All produced shelves should be sold.
Selling price cannot be changed because of competition. Unit prices of Model S and LX are $1800
and $2100 respectively.
Quantitive of products should be non-negativ
Constraints
-
Assembly capacity for Model S is 1900 units/month and for Model LX is 1400 units/month.
Available hours for stamping and forming are 800 hours/month.
Monthly production for Model S and LX should be greater or equal to zero.
Montly production for Model S and LX should be integer.
Some Necessary Formulas
Direct Labor Cost = sum of the direct labor costs from stamping, forming and assembly
Overhead Cost = sum of the overhead costs from stamping, forming and assembly
Total Cost = sum of the direct labor cost, overhead cost and direct material cost
Margin = The difference between unit selling price and total cost
Total Profit = Margin of S*Quantity of S + Margin of LX*Quantity of LX
OR
Total Profit = sum of the profit of each Model - Fixed costs
Total Time Required = sum of both model machine time requirement*Quantity
Analysis of Model
Let x and y represents the monthly production of Model S and Model LX respectively.
0.3x+0.3y ≤ 800 (Constraint available hours for stamping)
0.25x+0.5y ≤ 800 (Constraint available hours for forming)
x ≤ 1900 and y ≤ 1400 (Constraints for monthly production of Model S and Model LX)
x ≥ 0 and y ≥ 0 (Both monthly production should be an integer and ≥ zero)
and we want to maximize our total profit which is
(1800 - 1540)x + (2100 - 1855)y - 350.000
Unit Selling
Price of S
Direct Material Cost+Total Direct
Labor Cost+Variable Cost for S
Unit Selling
Price of LX
Fixed Cost
Direct Material Cost+Total Direct
Labor Cost+Variable Cost for LX
So, it is 260x + 245y - 350.000
CONCLUSION & INTERPRETATION
The calculation has proven that contribution margin of Model S is higher than Model LX. In conclusion, all
resources should be allocated to produce Model S up to its maximum production capacity.
In order to maximize the total profit, the monthly production plan should be 1900 unit/month for Model
S and 650 unit/month for Model LX. After arranging these optimal values by using “solver”, the total
profit would be $268,250 as you can see in Appendix II.
So, we can see that the engineer’s idea is wrong because he wanted to reduce the monthly production of
Model S in order to reduce lost per unit. If we reduce the monthly production of Model S, the total cost
of S will raise and it will reduce the total profit. By determining the Model S maximum, the production
will cover fixed costs, we will minimize our lost and therefore, total profit raises automatically.