$[20$:$36,21\mathrm{.}10\mathrm{.}2024]$ Ceren: Sound Products Company produces two lines of stereo equipment, Proline and Custom. These two regression equations have been developed to estimate quarterly sales for next year for the two products:

Y pro $=2,500-500$X Ycus $=625+500$X

where X represents the quarter $(1,2,3,4).$ All products must go through the flow$-$ soldering operation. This operation is the bottleneck operation for the entire factory, which means that this operation has the least capacity among all the operations in the entire facility. There are several flow$-$soldering machines in the operation, and only the num$-$ ber of machines required for production in a quarter is activated; the others remain in a deactivated status. Each flow$-$soldering machine can operate $200$ hours per quarter. It costs $$10,000$ to activate or deactivate a flow$-$soldering machine. Each activated flow$-$ soldering machine must be fully utilized; partial use is not economical $($round up to the next whole number of machines$).$ Each Proline product requires $1\mathrm{.}0$ hour of flow$-$ soldering$-$machine time, and each Custom product requires $0\mathrm{.}4$ hour of flow$-$soldering$-$ machine time. The company is now trying to decide if level capacity or matching demand would be the best aggregate capacity plan for producing the products. It costs $$50$ for every product of either type that is backlogged or placed in inventory at the end of a quar$-$ ter. The company begins the year with zero backlog and inventory. It is the company's policy, when demand exceeds production capacity, to satisfy the demand for Proline prod$-$ ucts within a quarter before the demand for Custom products is satisfied. When produc$-$ tion capacity exceeds demand, Custom products are produced with the excess capacity.

Assume that the quarterly demand pattern repeats from year to year.

$[20$:$41,21\mathrm{.}10\mathrm{.}2024]$ Ceren: AGGREGATE SOUND PRODUCTS COMPANY CASE

$1.$ Compute the quarterly aggregate flow soldering hours capacity required to meet sales demand for the two products

$2.$ Compute the number of flow soldering machines required in each quarter

$3.$ Use Level Plan to satisy the demand for the two products and compute the annual cost. $($Note: Use available capacity first to satisfy the demand for Pro Line and use remaining capacity to produce Custom and make sure to calculate the amount of capacity under$/$above the demand for each quarter$)$

$4.$ Use the Matching Demand plan, compute the cost of starting up and shutting down the flow soldering operation.

$5.$ Which plan do you prefer? Justify your preference with as many factors as posible.