$2$Question $2$: $(30\%)$SA Food Products Company owns several farms where it grows and harvests potatoes. It then ships$$these potatoes to three processing plants $($called A$,$ B$,$ C$)$ where different varieties of potato products,$$including chips, are produced. Recently, the company has experienced a growth in its product demand$$so it wants to buy one or more new farms to produce more potato products. The company is$$considering six new farms with the following annual fixed costs and projected harvest.$$Farms Fixed Annual Costs $($$$1,000$s$)$ Projected Annual Harvest $(1,000$ Tons$)140511\mathrm{.}2239010\mathrm{.}5345012\mathrm{.}843689\mathrm{.}3552010\mathrm{.}864659\mathrm{.}6$The company currently has the following additional available production capacity $($tons$)$ at its three$$plants that it wants to use: Plant A: $12$ thousands of tons, Plant B: $10$ thousands of tons, Plant C: $14$thousands of tons. The shipping costs $($$$)$ per ton from the farms being considered for purchase to the$$plants are as follows:$$Shipping Costs, $$/$ton$$Farm A B C$118151221310173161418419151651719126141612$The company wants to know which of the six farms it should purchase that will meet available$$production capacity at the minimum total cost, including annual fixed costs and shipping costs.$$Formulate a mathematical model and solve it using a computer, and what is the optimal solution?$3$Question $3$: $(30\%)$ABC company is a manufacturing company that has a contract to supply a customer with parts from$$April through September. However, ABC does not have enough storage space to store the parts during$$this period, so it needs to lease extra warehouse space during the six$-$month period. Following are$$ABC$$s space requirements.$$Month Required Space $($ft$2)$April $47,000$May $35,000$June $52,000$July $27,000$August $19,000$September $15,000$The rental agent that ABC is dealing with has provided it with the following cost schedule for$$warehouse space. This schedule shows that the longer the space is rented the cheaper it is$.$ For$$example$,$ if ABC rents space for all six months, it costs $$1\mathrm{.}00/$ft$2$ per month, whereas if it rents the$$same space for only month, it costs $$1\mathrm{.}70/$ft$2$ per month.$$Rental Period $($Months$)$ $$/$ft$2/$month$61\mathrm{.}0051\mathrm{.}0541\mathrm{.}1031\mathrm{.}2021\mathrm{.}4011\mathrm{.}70$ABC can rent amount of warehouse space on a month basis at any time for any number of $($whole$)$months$.$ ABC wants to determine the least costly rental agreement that will exactly meet its space$$needs each month and avoid any unused space.$($a$)$ Formulate a mathematical model for this problem, the space to rent is exactly the same as$$required$.($b$)$ Solve the model using a computer.$($c$)$ Suppose that ABC were to relax its restriction that it rent exactly the space it needs every$$month such that is would