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Problem $4-75$ and $4-76($Algo$)($LO $4-4,5)$

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Clarke Corporation manufactures three products $($X$-1,$ X$-2,$ and X$-3)$ utilizing, in one of the processes, a single machine for all products. Data on the individual products follow.

X$-1$ X$-2$ X$-3$

Price per unit $ $100$ $ $200$ $ $400$

Variable cost per unit $ $50$ $ $120$ $ $240$

Machine hours per unit $1\mathrm{.}02\mathrm{.}54\mathrm{.}0$

Maximum units demand per period $308,000154,00024,000$

The single machine used for all three products has a maximum capacity of $536,000$ hours per period.

Problem $4-76($Algo$)$ Theory of Constraints $($LO $4-5)$

Required:

a$.$ A local engineering firm claims it can revise the production process such that product X$-2$ only requires $1\mathrm{.}6$ machine hours on the shared machine. How much would Clarke be willing to pay per period for the new process?

b$.$ Suppose, instead, that the local engineering firm can revise the production process such that Product X$-3$ only requires $3\mathrm{.}5$ machine hours on the shared machine. $($Product X$-2$ requires $2\mathrm{.}5$ machine hours.$)$ How much would Clarke be willing to pay per period for the new process?