Linear Programming Assignment

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
Packagin
g Time
MR Drone $150 10 minutes 10 minutes 20
minutes