$($Exercise $2\mathrm{.}20$ from Rader textbook$)$ During the next $4$ months your company must meet $($on time$)$ the following demands for plastic garbage cans: $3000$ large and $2500$ small in month $1$; $4500$ large and $4000$ small in month $2$; $3000$ large and $4000$ small in month $3$; and $4000$ large and $4000$ small in month $4.$ At the beginning of month $1,75$ large and $50$ small cans are on hand. Each can is produced from plastic bought from another firm and must go through two different areas before completion. Each month, you are automatically shipped $30,000$ pounds of plastic to make the cans. Those cans not sold in a given month must be stored in a local storage facility. The table below gives the requirements for producing and storing each can, in addition to its production cost per unit. There are $650$ machine hours and $350$ painting hours available each month, as well as $10,000$ units of storage available. Production in a given month can be used to meet that month's demand. Formulate and solve a linear program to determine the optimal production schedule.