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 works 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. Determine how to minimize the cost of meeting (on time) the demands of the next six months.

Use the following template to solve this.

A1 fx Shoemakers of America \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline & A & B & C & D & E & F & G & H \\ \hline 1 & Shoemakers of America & & & & & & & \\ \hline \multicolumn{9}{|l|}{2} \\ \hline 3 & Hours/worker/pair of shoes & 0.333333 & & & & & & \\ \hline 4 & Regular time hours/month & 150 & & & & & & \\ \hline 5 & Maximum overtime hours/month & 40 & & & & & & \\ \hline \multicolumn{9}{|l|}{6} \\ \hline 7 & Regular salary per month & $2,000 & & & & & & \\ \hline 8 & Overtime hourly pay & $20 & & & & & & \\ \hline 9 & Cost to hire a worker & $1,000 & & & & & & \\ \hline 10 & Cost to fire a worker & $1,200 & & & & & & \\ \hline \multicolumn{9}{|l|}{11} \\ \hline 12 & Raw material cost/pair of shoes & $10 & & & & & & \\ \hline 13 & Holding cost (\% of regular-time cost) & 5% & & & & & & \\ \hline \multicolumn{9}{|l|}{14} \\ \hline 15 & Initial number of workers & 15 & & & & & & \\ \hline 16 & Initial inventory & 500 & & & & & & \\ \hline \multicolumn{9}{|l|}{17} \\ \hline 18 & Production/hiring/firing schedule & & & & & & & \\ \hline 19 & Month & 1 & 2 & 3 & 4 & 5 & 6 & \\ \hline 20 & Workers from previous month & & & & & & & \\ \hline 21 & Workers hired & & & & & & & \\ \hline 22 & Workers fired & & & & & & & \\ \hline 23 & Workers available & & & & & & & \\ \hline \multicolumn{9}{|l|}{24} \\ \hline 25 & Regular-time hours & & & & & & & \\ \hline 26 & Overtime hours & & & & & & & \\ \hline \multicolumn{9}{|l|}{27} \\ \hline 28 & Maximum overtime hours & & & & & & & \\ \hline \multicolumn{9}{|l|}{29} \\ \hline 30 & Total hours available & & & & & & & \\ \hline \multicolumn{9}{|l|}{31} \\ \hline 32 & Shoes produced & & & & & & & \\ \hline \multicolumn{9}{|l|}{33} \\ \hline 34 & Production capacity & & & & & & & \\ \hline \multicolumn{9}{|l|}{35} \\ \hline 36 & Shoes available after production & & & & & & & \\ \hline \multicolumn{9}{|l|}{37} \\ \hline 38 & Demand & 5000 & 6000 & 7000 & 9000 & 6000 & 5000 & \\ \hline 39 & Ending inventory & & & & & & & \\ \hline \multicolumn{9}{|l|}{40} \\ \hline 41 & Regular salary cost & & & & & & & \\ \hline 42 & Overtime cost & & & & & & & \\ \hline 43 & Hiring cost & & & & & & & \\ \hline 44 & Firing cost & & & & & & & \\ \hline 45 & Raw material cost & & & & & & & \\ \hline 46 & Holding cost & & & & & & & \\ \hline 47 & Total cost & & & & & & & \\ \hline \end{tabular}