A craftsman of string instruments has received a new order to craft violins and guitars. The craftsman haslimited resources (wood, string, varnish) and time available to create the instruments. Each type of instrument(violin and guitar) requires specific amounts of these resources as well as a certain amount of time to complete.The craftsman wants to find the optimal number of violins and guitars to create in order to maximize the profitfrom selling them, while respecting the resource and time constraints (all instruments will be sold).The profit from selling each violin is 6,000 NOK, and the profit from selling each guitar is 3,000 NOK.Each violin requires 4 kg of wood, 0.3 l of varnish, and 2 m of string, and takes 3 days to craft. For eachguitar, the craftsman needs 5 kg of wood, 0.1 l of varnish, and 6 m of string, and it takes 2 days to make it.The craftsman’s workshop is stocked with 60 kg of wood, 2.5 l of varnish, and 65 m of string. The order needsto be completed in 30 days.Your task is to find the optimal number of instruments to make for the craftsman! Draw this constrainedoptimization problem, and use linear programming graphically to determine the optimal numbers of guitarsand violins to maximize the profit. Is the optimum unique? If not, how would they compare to each other?Additionally, calculate the expected (maximal) profit and how much of the materials will be left aftercompleting the order. What would be the maximal profit be, if fractional instruments could be produced andsold (maybe a guitar missing a few strings, or half a violin)?
A craftsman of string instruments has received a new order to craft violins and guitars. The craftsman has
limited resources (wood, string, varnish) and time available to create the instruments. Each type of instrument
(violin and guitar) requires specific amounts of these resources as well as a certain amount of time to complete.
The craftsman wants to find the optimal number of violins and guitars to create in order to maximize the profit
from selling them, while respecting the resource and time constraints (all instruments will be sold).
The profit from selling each violin is 6,000 NOK, and the profit from selling each guitar is 3,000 NOK.
Each violin requires 4 kg of wood, 0.3 l of varnish, and 2 m of string, and takes 3 days to craft. For each
guitar, the craftsman needs 5 kg of wood, 0.1 l of varnish, and 6 m of string, and it takes 2 days to make it.
The craftsman’s workshop is stocked with 60 kg of wood, 2.5 l of varnish, and 65 m of string. The order needs
to be completed in 30 days.
Your task is to find the optimal number of instruments to make for the craftsman! Draw this constrained
optimization problem, and use linear programming graphically to determine the optimal numbers of guitars
and violins to maximize the profit. Is the optimum unique? If not, how would they compare to each other?
Additionally, calculate the expected (maximal) profit and how much of the materials will be left after
completing the order. What would be the maximal profit be, if fractional instruments could be produced and
sold (maybe a guitar missing a few strings, or half a violin)?
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