C$.$ Calculate the profit. $(2$ points$)$

A steel product is manufactured by starting with raw material $($carbon steel wire$)$ and

then processing it sequentially through five operations using machines $A$ to $E,$

respectively $($see following table$).$ This is the only use that the five machines are put to$.$

The hourly production rates for each machine are given in the table.

Sol cookie company produces cookies and following are the different stages in their

cookie making and selling process. The company has five resources or workers $($one

Mixer, one Baker, one Cooler, one Packer, and one Payment Processor$)$ performing the

activities as shown in the diagram below and each of them can perform only their

respective activity. Each resource is available for a week.

The orders compiled for the next week are as follows:

Choco$-$chips cookie $-15$ boxes

Raisin$-$dates cookie $-22$ boxes

Almond cookie $-15$ boxes

The following table provides the details about the price and costs pertaining to different types of

cookies:

Time taken for all the three types of cookies are given below in mins $/$ box:

The fixed operating expenses for a week $($eight$-$hour day and five days a week$)$ is $$2000.$

A$.$ Is there a bottleneck $($constraint$)?$ If so$,$ which resource is a bottleneck $($constraint$)?(4$

points$)$ You need to show your calculations.

B$.$ Determine the product mix $($type of cookie and how many boxes for each type$)$ that

would maximize the profit. $(7$ points$)$ You need to show your calculations.