A manufacturer of rotary pumps is planning production for thc next four months. The forecast demand for the rotary pumps is shown in the following table.
Rotary pump SEP OCT NOV DEC
Standard 650 875 790 1,100
Heavy duty 900 350 1.200 1,300
At the beginning of September, the warehouse is expected to be complctcly empty. There is room for no more than 1.800 rotary pumps to be stored. Holding costs for both types arc S5 per unit per month. llecausc workers are given time off during thc holidays. thc manufacturer wants to havc at least 800 standard rotary pumps and 850 heavy duty rotary pumps alrcady in the warehouse at the beginning of January.
Production costs are $125 per unit for standard rotary pumps and $135 per unit for hcavy duty rotary pumps.
liccause demand for raw materials is rising. production costs arc cxpccted to risc by 5% per month through the end of the year.
Labor to make the standard rotary pump is 0.45 hours per unit; making heavy duty rotary pumps takes 0.52 hours per unit of labor. Management has agreed to schedule at least I ,0(X) hours per month of labor. As many as 200 extra hours per month are available to management at the same cost, except during the month of December. when only 100 extra hours are possible.
Formulate the given problem scenario as a linear program so as to determine the production schedule for standard and heavy duty rotary pumps for the four months. Solse the problem using Microsoft Excel with ASPE. For the formulation, provide a complete description of the decision variables used along with their units and also label the constraints mentioned in the problem as completely as possible. Also, the spreadsheet model setup should providc clearly labeled values used for the decision variables, constraints, and objective function.
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