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# Linear Programming of Automobile Sales

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A major automobile manufacturer also produces two types of trucks type I and typeII. all the trucks are produced in one plant in the eastern part of the united states. each month the production manager of the plant must detemine how many units of each truck to produce. The type I truck generates a contribution margine of \$220 per unit whereas on the type II truck a contibution margin of \$420 is realized. The production of both trucks must go through the following phases: engine construction, chassis assembly and inspection. Production requirements for type I truck are 3 hours of engine construction 8 hours of chassis assembly and 2 hours of inspection. The production of a type II truck requires 9 hours for engine construction 5 hours for chassis assembly and 3 hours for inspection. The production manager has available each month 8,100 hours for engine construction 12,000 hours for chassis assembly and 3,600 hours for inspection. The sales department informs the production manager that demand is sufficient to handle any number of type I trucks produced, however only 800 type II trucks can be sold. Assuming the production manager wishes to maximize the toatal contribution margin, please answer the following questions.
a) formulate a linear program with objectives and constraints and clearly identify all variables and constraints.
b) graph this program identifying the feasible region and potential optimal solutions.
c) what is the optimal combination of trucks that should be produced?
d) compute the shadow price for each of the constraints and verbally describe what these values mean.
e) if the production manager was given an opporunity to spend and additonal \$1000 on advertising to increase demand for the ypeo II truck should he implement the plan? please explain.

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