Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each...

 

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Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, und tractor assembly are given in the table. Assembly Machine Shop 2 bours 1 hour G0 hours Fabrication 2 hours 3 hours Tractor Thour O hour Lawn Mower Hrs. Available 120 hours 45 hour Formulation: Let x number of tractors produced per period y = number of lawn mowers produced per period 30x + 30y 2x +y S 60 2x + 3ys 120 XS 45 The graphical solution is shown below. MAX subject to 70 50 40 20. 10 60 70 10 a) How many tractors and saws should be produced to maximize profit, and how much profit will they make? b) Determine the sensitivity range for the profit for tractors. c) What is the shadow price for assembly? d) What is the shadow price for fabrication? e) What is the maximum amount a manager would be willing to pay for one additional hour of machining time? f) A breakdown in fabrication causes the available hours to drop from 120 to 90 hours. How will this impact the optimal number of tractors and mowers produced? g) What is the range for the shadow price for assembly? Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, und tractor assembly are given in the table. Assembly Machine Shop 2 bours 1 hour G0 hours Fabrication 2 hours 3 hours Tractor Thour O hour Lawn Mower Hrs. Available 120 hours 45 hour Formulation: Let x number of tractors produced per period y = number of lawn mowers produced per period 30x + 30y 2x +y S 60 2x + 3ys 120 XS 45 The graphical solution is shown below. MAX subject to 70 50 40 20. 10 60 70 10 a) How many tractors and saws should be produced to maximize profit, and how much profit will they make? b) Determine the sensitivity range for the profit for tractors. c) What is the shadow price for assembly? d) What is the shadow price for fabrication? e) What is the maximum amount a manager would be willing to pay for one additional hour of machining time? f) A breakdown in fabrication causes the available hours to drop from 120 to 90 hours. How will this impact the optimal number of tractors and mowers produced? g) What is the range for the shadow price for assembly?

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