$6\mathrm{.}2$ You are tying to bake $3$ 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 $325$ F $(160$ 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.

$6\mathrm{.}2\mathrm{.}1$ Your job is to cook $3$ cakes as efficiently as possible. Assuming that you only have one oven large enough to hold one cake, one large bowl, one cake pans, and one mixer, come up with a schedule to make three cakes as quickly as possible. Identify the bottlenecks in completing this task.

$6\mathrm{.}2\mathrm{.}2-$ Assume now that you have three bowls, $3$ cake pans and $3$ mixers. How much faster is the process now that you have additional resources?

$6\mathrm{.}2\mathrm{.}3$ 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?

$6\mathrm{.}2\mathrm{.}4$ Compare the cake$-$making task to computing $3$ iterations of a loop on a parallel computer. Identify data$-$level parallelism and task$-$level parallelism in the cake$-$making loop.