Linear Programming Assignment: Kingston Consumer Goods Analysis

This assignment focuses on a linear programming problem faced by Kingston Consumer Goods, a drone manufacturer. The core objective is to determine the most profitable daily production plan for two drone types (MR and SR) considering constraints on assembly, testing, and packaging machine time. The solution utilizes Excel Solver to optimize production and provides a detailed sensitivity analysis. The analysis explores how changes in resource availability (packaging, testing, and assembly machine time) and profit margins affect the optimal production plan and overall profit. Furthermore, the assignment investigates the potential inclusion of a third drone type (FW) and determines the minimum profit contribution required for its consideration. The solution provides insights into how the optimal solution changes with varying parameters and the impact of constraints on the company's profitability.

LINEAR PROGRAMMING
ASSIGNMENT

1. Kingston Consumer Goods
A drone manufacturer produces 2 types of drones, the multi-rotor (MR), and the
single-rotor (SR). The profit margin is $150 per unit for MR drones and $200 per
unit for SR drones. One assembly machine is used to produce both models, and it
operates for 600 minutes each day. An MR unit needs 10 minutes in the assembly
machine, and an SR unit needs 30 minutes. The drones also need to be tested, and
are both types are tested on the same machine, which operates for 600 minutes
each day. An MR unit requires 10 minutes of testing machine time, and an SR unit
needs 20 minutes. The last phase of production is packaging, and both products are
packaged on the same packaging machine and both drone types takes 20 minutes to
pack. Determine the most profitable daily production plan and answer the
following questions using the sensitivity report generated by Excel solver only. a)
If the packaging machine has 1000 minutes available (instead of 600), how will the
optimal solution change? b) If the testing machine has 500 minutes available, by
how much will the optimal profit change? c) If the assembly machine has 1000
minutes available, by how much will the optimal profit change? d) If the profit
margin for MR is $200 per unit, how will the optimal profit change? How will the
optimal decision variables change? e) If the profit margin for SR is $100 per unit,
how will the optimal solution change? f) The company is also capable of producing
a third type of drones, fixed-wing (FW) drones. FW drones needs 10 minutes for
assembly, 20 minutes for testing and 15 minutes for packaging. Based on your
existing information (i.e., without reformulating your optimization model), what is
the minimum profit contribution per unit for the FW drones that would incent the
company to consider producing them in addition to the two existing products?
Note: There are 3 separate machines that share the same resource pool.
Solution:
Summarization of the problem:
Drones Profit Margin Assembly
Machine Time
Testing time Packaging
Time
MR Drone $150 10 minutes 10 minutes 20 minutes
SR Drone $200 30 minutes 20 minutes 20 minutes

Availability -------- 600 minutes 600 minutes 600 minutes
Excel Screenshot for solving the Model:
Sensitivity Report of the Excel Solver:
(a) If the available packaging time changes from 600 minutes to 1000 minutes, the
profit will increase from $5250 to $7750 and the number of MD Drones and SR
Drones will be changed to 45 and 5 from 15 each, respectively. There is allowable
increase of 600 minutes and thus we can go upto 1200 minutes in the packaging
time for more optimization, as interpreted from the sensitivity report.
(b) If the available testing time is 500 minutes, the profit will increase from $5250
to $7500 as the constraint will become a binding constraint. There is allowable

decrease of 150 minutes in the testing time and thus it will optimize the profit if
we decrease by 100 minutes.
(c) If we change assembly machine time to 1000 from 600 minutes, as the
allowable increase is only 300 minutes and the shadow price is $2.5, the profit
increase will be 300*2.5 = $750. The total profit will be $5250 + $v750 = $6000.
(d) The profit will increase from $5250 to $6000. Earlier, MR Drones and SR
Drones were 15 units respectively. After increasing the profit of MR Drones from
$ 150 to $200, the decision variables be 30 and 0 respectively.
(e) There is allowable decrease of only $50, so the profit will reduce if we reduce
the profit by $100. The profit will reduce to $4500 from $5250.
(f)The given constraints do not allow a third type of product in the existing
problem.