Linear Programming Project: Cocoa Powder Usage and Profit Maximization

This project utilizes linear programming to analyze and optimize chocolate production processes. The assignment begins by determining the number of boxes required for different chocolate products and formulates a linear program to maximize profit based on resource constraints. The analysis then delves into cocoa powder usage, highlighting inefficiencies in a fixed-volume agreement and proposing a shift to a variable-volume contract to reduce waste and costs. Negotiation strategies for a new pricing model are discussed. Furthermore, the project assesses the impact of acquiring additional cocoa powder, demonstrating the increase in production and profit. The solution includes a decision table summarizing financial data and a bibliography of relevant research. The project emphasizes optimizing resource allocation and making informed business decisions within the context of chocolate manufacturing.

Running head: LINEAR PROGRAMMING
Linear Programming
Name of the Student:
Name of the University:
Author’s Note:

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Table of Contents
Requirement 1:.................................................................................................................................2
Requirement ii:................................................................................................................................2
Requirement iii:...............................................................................................................................3
Requirement iv:...............................................................................................................................4
Requirement v:.................................................................................................................................4
Requirement vi:...............................................................................................................................5
Decision Table:................................................................................................................................5
Total Net Profit:...............................................................................................................................6
Total Contribution:..........................................................................................................................7
Bibliography....................................................................................................................................8

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Requirement 1:
In order to have an idea about the number of boxes that would produced for each of the product,
it is seen that 33333 boxes would be required in order to pack the premium chocolate bars and
80000 boxes would be required in order to pack the dark couverture. In case of packing the
chocolate sauce, there are no boxes required and therefore in an overall manner it is observed
that there is a requirement of 113333 boxes in order to pack all the chocolates and thereafter
offer for sales in the market. The linear program for the same is given below:
Max 12A + 14B + 11C
Where, 0.18A <= 6000 kgs.
0.2B <= 30000 kgs.
0.25C <= 24000 kgs.
0.18A + 0.2B + 0.25C <= 30000 kgs.
Requirement ii:
In accordance to this question, it is seen that the total amount of cocoa powder that is
purchased for the purpose of manufacturing is 30000 units and the overall expense for the same
is $540,000. However, it is observed that the overall consumption of cocoa that is used in order
to manufacture the chocolate bars, chocolate sauce and dark couverture is seen to be 25999.94
units. Therefore there has been an observation that approximately 4000 units of cocoa remains
unused and therefore gets wasted and the cost that is associated with that amount of cocoa is an

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additional expense. Therefore, steps and strategies need to be taken with the help of which the
wasted cocoa can be used or this amount can be reduced as well.
Particulars Unit Amount
Grade A 6000 $1,08,000
Grade B 24000 $4,32,000
Total Cocoa Powder (in kgs.) 30000 $5,40,000
Additional Cocoa (in kgs.) 800
Total Cocoa Powder (in kgs.) 30800 $5,40,000
Optimum Product Mix:
Particulars Premium Bars
Chocolate
Sauce
Dark
Couverture
Total
Consumption
Maximum Demand 37777 50000 80000
Sales Volume (in box) 37777 0 80000
Cocoa Powder (kgs/Box) 0.18 0.2 0.25
Total Cocoa Powder Required 6799.86 0 20000 26799.86
Requirement iii:
It is seen that in accordance to the current strategy which is a fixed volume agreement, there
has been wastage of approximately 4000 units of cocoa for which a certain amount of money is
invested. The maintenance of the fixed volume agreement refers to the fact that in each month
and year the company would be purchasing the same unit of cocoa irrespective of the fact that
whether they are able to optimally make use of the total amount of cocoa purchased. Hence, it is
agreeable that variable volume contract can be taken into consideration. Therefore, it would be
better for the company to shift their intention from the fixed volume agreement to the variable
volume of contract in which the company would be able to purchase the raw material based on

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the demand in the market and the amount of production they would undertake. In this manner,
the unit of cocoa can vary according to the demand of the final product and thereby the amount
of wastage can be reduced and the additional cost that was added with the wasted material can be
mitigated. It is even seen that the company would be able to optimally make use of their
resources and in this manner would be able to enhance their operational activities and their
effectiveness in production.
Requirement iv:
In case variable volume contract is undertaken, it would be essential for Steve to negotiate a
different pricing model because of the fact that the supplier want to sell a specific amount of unit.
In this manner, the incorporation of a different pricing model is essential with the help of which
an effective price for the product can be created with the help of which the supplier is able to
gain certain amount out of the expected money they have anticipated and a price that would be
over the actual rate but would be less than the overall money paid earlier which was inclusive of
the unit of cocoa that remained wasted. A price that would be able to satisfy the demands of the
customer and the supplier would be an effective one for the maintenance of the current
relationship and none of them facing an impact for the change in the purchase agreement.
Requirement v:
By assessing the scenario of taking up an additional 800 kg of Grade A powder at the same cost
that was paid earlier it is seen that the amount of production would increase and the overall
consumption of use of the cocoa powder would increase from 25999.94 units to 26,799.86 units.
In this manner it is seen that the overall consumption would increase and there would be a rise in
the total net profit for the company by $1,600. Hence, taking up the additional 800 kg would be

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beneficial. The company can purchase 6000 units by not changing the basis of the solution. The
linear program for the same is stated below:
Max 12A + 14B + 11C
Where, 0.18A <= 6800 kgs.
0.2B <= 30000 kgs.
0.25C <= 24000 kgs.
0.18A + 0.2B + 0.25C <= 30800 kgs.
Requirement vi:
The extent of sensitiveness for the preferred product is similar to the product mix that
was available earlier because of the fact that with the addition of the extra 800 kg only the extent
of overall consumption has changed but the sales and cost has remained similar to the one that
was seen earlier.
Decision Table:
Premium Bars
Total
Revenue
3333 Boxes x
$12
$1,311,996
Chocolate Sauce
0 boxes x $14
Profit
$40,800
Dark
Couverture
80000 Boxes x

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$11
Direct Labor
$247,599
Variable
Overhead
$86,400
Total Cost
$1,271,196 Variable Selling
$131,200
Cocoa
$467,999
Packaging
$254,799
Allocated
Overhead
$71,999

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Total Net Profit:
Computation of Net Profit:
Particulars Premium Bars
Chocolate
Sauce
Dark
Couverture TOTAL
Total Sales Revenue $3,99,996 $0 $9,12,000 $13,11,996
Direct Labor $1,17,999 $0 $1,29,600 $2,47,599
Variable Overhead $24,000 $0 $62,400 $86,400
Variable Selling $40,000 $0 $91,200 $1,31,200
Cocoa $1,07,999 $0 $3,60,000 $4,67,999
Packaging $69,999 $0 $1,84,800 $2,54,799
Allocated Overhead $28,000 $21,000 $23,000 $71,999
Total Costs $3,87,996 $0 $8,83,200 $12,71,196
Net Profit $12,000 $0 $28,800 $40,800
Total Contribution:
Computation of Contribution Margin:
Particulars Premium Bars
Chocolate
Sauce
Dark
Couverture TOTAL
Total Sales Revenue $3,99,996 $0 $9,12,000 $13,11,996
Direct Labor $1,17,999 $0 $1,29,600 $2,47,599
Variable Overhead $24,000 $0 $62,400 $86,400
Variable Selling $40,000 $0 $91,200 $1,31,200
Cocoa $1,07,999 $0 $3,60,000 $4,67,999
Packaging $69,999 $0 $1,84,800 $2,54,799
Contribution Margin $40,000 $0 $84,000 $1,24,000

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Bibliography
Ezzati, R., Khorram, E. and Enayati, R., 2015. A new algorithm to solve fully fuzzy linear
programming problems using the MOLP problem. Applied mathematical modelling, 39(12),
pp.3183-3193.
Zhang, Y., Sun, X. and Wang, B., 2016. Efficient algorithm for k-barrier coverage based on
integer linear programming. China Communications, 13(7), pp.16-23.