You are trying to bake three blueberry pound cakes. Cake ingredients are as follows:

$1$ cup butter, softened

$1$ cup sugar

$4$ large eggs

$1$ teaspoon vanilla extract

$1/2$ teaspoon salt

$1/4$ teaspoon nutmeg

$11/2$ cups flour

$1$ cup blueberries

The recipe for a single cake is as follows:

Step $1$: Preheat oven to $325\backslash$deg F $(160\backslash$deg C$).$ Grease and flour your cake pan.

Step $2$: In large bowl, beat together with a mixer butter and sugar at medium speed until light and fluffy. Add eggs, vanilla, salt and nutmeg. Beat until thoroughly blended. Reduce mixer speed to low and add flour, $1/2$ cup at a time, beating just until blended.

Step $3$: Gently fold in blueberries. Spread evenly in prepared baking pan. Bake for $60$ minutes.

$($a$)$

Your job is to cook three cakes as efficiently as possible. Assuming that you only have one oven large enough to hold one cake, one large bowl, one cake pan, and one mixer, come up with a schedule to make three cakes as quickly as possible. Identify the bottlenecks in completing this task.

$($b$)$

Assume now that you have three bowls, three cake pans and three mixers. How much faster is the process now that you have additional resources?

$($c$)$

Assume now that you have two friends that will help you cook, and that you have a large oven that can accommodate all three cakes. How will this change the schedule you arrived at in Exercise $6\mathrm{.}2\mathrm{.}1$ above?

$($d$)$

Compare the cake$-$making task to computing three iterations of a loop on a parallel computer. Identify data$-$level parallelism and task$-$level parallelism in the cake$-$making loop.