Prepare algebraic and mathematical LP model

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Reference no: EM132297961

Shoemakers of America forecasts the following demand for the next six months: 5000 pairs in month 1; 6000 pairs in month 2; 7000 pairs in month 3; 9000 pairs in moth 4; 6000 pairs in month 5; 5000 in month 6. It takes a shoemaker 20 minutes to produce a pair of shoes. Each shoemaker worsk 150 hours per month plus up to 40 hours per month of overtime. A shoemaker is paid a regular salary of $2000 per month plus $20 per hour of overtime. At the beginning of each month, shoemakers can either hire or fire workers. It costs the company $1000 to hire a worker and $1200 to fire a worker. The monthly holding cost per pair of shoes is 5% of the cost of producing a pair of shoes with regular time labor. The raw materials in a pair of shoes cost $10. At the beginning of month 1, shoemakers has 15 workers and 500 pairs of shoes in inventory.

Prepare an algebraic/mathematical LP model that helps minimize the total cost of meeting (on time) the demands of the next six months. Type your model in a Word document.

In an Excel file, convert the algebraic model you developed above into an Excel model; and then use Solver to find the optimal solution.

Remark: for each month, calculate the holding cost based on the ending inventory of that month.

Reference no: EM132297961

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