Problem $4$

Schmidt Industries makes four different snake traps; the Harlan, the Gaylen, the Leah and the Matthew.

The Harlan sells for $$200$ and has $$40$ in parts and $$40$ in labor; the Gaylen sells for $$150$ and requires $$30$

in parts and $$30$ in labor; the Leah sells for $$100$ and has $$20$ in parts and $$20$ in labor; and the Matthew

sells for $$75$ but requires only $$10$ of parts and $$10$ of labor. Schmidt Industries has four machines $($we$\text{'}$ll

call them A$,$ B$,$ C$,$ and D for convenience$)$ that are used in the production of each of these products. Each

of these machines is available for $40$ hours a week and there is no setup time required when shifting from

the production of one product to any other. The processing requirements to make one unit of each

product are shown in the table.

Schmidt Industries has weekly fixed costs of $$5,000$ and has a demand forecast of $80$ Harlans, $60$ Gaylens,

$40$ Leahs and $20$ Matthews for the coming week. Determine how many of each of the four models Susan,

the operations manager, should schedule for production this week under each of the following

approaches:

a$)(10$ points$)$ Using the traditional method, which bases decisions solely on a product's contribution

to profits and overhead, what is the optimal product mix? What is the associated overall

profitability?

b$)(15$ points$)$ What is the bottleneck operation? Using the bottleneck$-$based approach, what is the

optimal product mix? What is the associated overall profitability?