Problem $2(25$ pts$)$

You're building a startup that manufactures wooden toy airplanes. You've built a decent

reputation in your area and already know the demand for the next three months: $500,600,$ and

$400$ airplanes, respectively.

You have found two suppliers of wood near your area. Each supplier can provide at most $405$

loads of wood each month. The price of buying one load of wood for one toy airplane at each

supplier in each month is shown in the table below.

Your friend has a shed where you can store extra loads of wood at the end of each month, but it

comes at a cost of $$5$ per load of wood per month.

a$)$ Develop a linear program to determine an optimal purchasing plan for the next three months

to ensure demand is met each month. Write out the LP in full $($no i$\text{'}$s$,$ no j$\text{'}$s$,$ no sigmas$).(15$ pts $)$

b$)$ Your suppliers have not been very reliable this past month. So$,$ you're considering buying old

wooden toys and re$-$purposing them into toy airplanes. Each old wooden toy you buy can be

transformed into one toy airplane. To avoid losing any of your suppliers, you cannot buy more

EM$333-$HW$1-$F$24$

old wooden toys than loads of wood. Given this new information, make any necessary changes

to the LP found in part a$.$ Be sure to also explain in words what changes were made. $(10$ pts$)$