$($Make$-$or$-$buy decision$)$ Larkin Industries manufactures several lines of decorative and functional metal items. The most

recent order has been for $1200$ door lock units for an apartment complex developer. The sales and production departments

must work together to determine delivery schedules. Each lock unit consists of three components: the knob and face plate, the

actual lock itself, and a set of two keys. Although the processes used in the manufacture of the three components vary, there

are three areas where the production manager is concerned about the availability of resources. These three areas, their usage by

the three components, and their availability are detailed in the table. $(30$ pts $)$

A quick look at the amounts available confirms that Larkin does not have the resources to fill this contract. A subcontractor,

who can make an unlimited number of each of the three components, quotes the prices below.

Develop a linear programming model that would tell Larkin how to fill the order for $1200$ lock sets at the minimum cost.

Bonus Question $(20$ pts$)$:

excel

$($Production scheduling$)$ develop the linear programming model.

Greenville Cabinets received a contract to produce speaker cabinets for a major speaker manufacturer. The contract calls for

the production of $3300$ bookshelf speakers and $4100$ floor speakers over the next two months, with the following delivery

schedule:

Greenville estimates that the production time for each bookshelf model is $0\mathrm{.}7$ hour and the production time for each floor

model is $1$ hour. The raw material costs are $$10$ for each bookshelf model and $$12$ for each floor model. Labor costs are $$22$

per hour. Greenville has up to $3400$ hours of production time available each month. If production for either cabinet exceeds

demand in month $1,$ the cabinets can be stored at a cost of $$5$ per cabinet. For each product, determine the number of units

that should be manufactured each month to minimize total production and storage costs.