QR 26: Choice and Chance

The Mathematics of Decision Making

 

Unit III Activity Name:_________________
  1. You are in charge of planning your residence hall's meals for one week. As you think of your objectives when planning the meals, what quantitative aspects of the meals would you like to optimize? Give as many examples as you can think of.

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  2. Now you're a baker at a bakery, which produces two products: Eclairs and Napoleons. Each eclair needs 3 ounces of custard and takes 7.5 minutes to make. Each Napoleon needs 1 ounce of custard and takes 15 minutes to make. You work a maximum 10- hour day and you only have 120 ounces of custard to work with. What combinations of eclair production and Napoleon production are possible, and which of these could, for some set of prevailing pastry prices, maximize the revenue you collect per day?

Mark each combination of eclairs and Napoleons with a "F" if it's a feasible answer, meaning it does not violate any of the rules of the problem. Further, mark a combination with an "O" if it's possible that combination could maximize profit. Briefly justify your answers.

a. ___ 80 eclairs, 0 Napoleons

b. ___ 0 eclairs, 120 Napoleons

c. ___ 40 eclairs, 0 Napoleons

d. ___ 32 eclairs, 24 Napoleons

e. ___ 20 eclairs, 20 Napoleons

f. ___ 10 eclairs, 60 Napoleons

g. ___ 5 eclairs, 30 Napoleons

h. ___ 0 eclairs, 40 Napoleons

i. ___ 60 eclairs, 5 Napoleons

 

 

 

 

 
  1. Your boat company makes four different kinds of boats: Large sailboats (at $1200 profit per boat), small sailboats (@ $930), motorboats (@ $1050) and sailboards (@ $750). Each boat requires some of your raw materials on hand, according to the table that follows. Explain below your answers to the following three questions:
   

Requirements by Product

Raw Materials

On Hand

Large Sailboat

Small Sailboat

Motorboat

Sailboard

Sailcloth

700

4

3

0

1

Glass Fiber

1,380

8

3

4

2

Epoxy Resin

1,280

3

3

3

2

Aluminum

1,100

4

2

2

2

Engines

120

0

0

1

0

 

a. What will be your total profit if you devote all your resources to making your most profitable boat? Is this a good plan?

 

 

 

 

b. Specifically, could you make a swap in your production plan to increase your total profit? If not, why not? If so, by how much? Have you found the best plan yet?

 

 

 

 

c. If you could have a bit more of one raw material, which do think would do you the most good? How much would you be willing to pay for an extra unit of it?