Shelby Shelving Company

The function of this analysis is to maximize revenue of Shelby Shelving Business, manufacturing 2 kinds of shelves for supermarket; Model S (basic model) and Design LX (heavy duty model). The plant's engineer suggested that Model S manufacturing need to be cut off as they are sold less than their production cost. On contrary the controller argued that Design S items take in a big manufacturing overhead burden so even though they are sold at loss, their production needs to continue. The analysis is performed by provided accounting and production information for Shelby Company.

Taking a look at particular information initially glance, reducing Design S production and increasing Model LX production appears to be practical as system earnings for Model S is less than that of Design LX.

Nevertheless a strenuous analysis performed by Microsoft Excel with Solver Add-in indicated that for optimum revenue increasing production of design S to its assembly capability limitation. The reasoning behind this outcome is that Design S has lower direct material, direct labour cost and variable overhead cost than Design LX so producing more Model S will allow company to compensate fixed assembly expense better.

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As a result increasing Model S production approximately its assembly capacity and determining production of Model LX based upon constraints gives us finest option. Therefore the argument of the controller is more affordable than that of the plant's engineer.

MODELLING

Presumptions
a) All of the products are sold.
b) Selling prices of Model S and Model LX are constant and cannot be changed as a result of competition.

c) There are no machine breakdowns or out of operation periods so hour spent in stamping and forming departments are constant for respective products.
d) Direct material cost (per unit), direct labour cost (per unit), fixed overhead costs (per unit), and variable overhead costs per unit
e) There are no advance payments received for delivering products later on so quantities of products are non-negative.

Decision Variables

a) Current monthly production of Model S
b) Current monthly production of Model LX
Objective
Maximize the profit
Constraints
a) The hours spent in departments must not exceed the available stamping and forming labor hours.
b) The monthly production must not be greater than the assembly capacity of the plant.

Algebraic Model

Objective:
MAX { ((PS*QS - PS*VCS) - FC) + ((PLX*QLX - PLX*VCLX) - FC) };

Constraints:
a) Stamping:0.3*Qs + 0.3*QLX