9781118041581

Summary 743

as blood pressure and cholesterol. Both scales have been developed by

the Office of the U.S. Surgeon General. The last column lists the

Surgeon General’s recommended goals for a healthy weekly diet, 70 for

BMI and 80 for heart.

Healthy Standard Fast Food Restaurant Diet Score

Portions 0.25 0.25 0.25 0.25

Value $3.00 $8.00 $12.00 $28.00 $12.75 Goals

Cost $6.00 $5.00 $8.00 $20.00 $9.75 $10.00

BMI 100 70 20 50 60.00 70

Heart 100 70 40 70 70.00 80

The Cost row lists the average cost per meal (from a database of

cities across the United States. (The costs in the table are those for

Milwaukee, Wisconsin.) Finally, the values in the first row are purely

personal and have been entered by the financial analyst himself. (Notice

that the analyst’s taste buds are quite averse to healthy meals. He rates a

$6.00 healthy meal as worth only $3.00 in value.)

At the outset, the app sets the meal proportions by default at .25

across the board. (You might think of the individual as eating 6 or 7

meals per week in each category.) For these default proportions, the

diet column calculates the average cost, BMI score, and heart score per

meal. (These scores are computed by multiplying each meal category

proportion by its score and then adding these products over the four

categories.) Note that the default diet falls short of meeting both the

BMI and heart goals listed in the last column.

a. On a spreadsheet, re-create this app in the form of a linear program.

b. Use your spreadsheet’s optimizer to find the meal proportions that

meet the BMI and heart goals at minimum cost. Which category is not

a part of the least-cost weekly meal plan?

c. Instead, the analyst wants to adopt a plan that maximizes his value per

meal while meeting both health goals and spending no more than $10

per meal on average. Use the optimizer to determine this meal plan.

How does the plan change if the analyst is able to budget $15 per meal?

11. A Boston-based middle manager recently received an exciting e-mail
    offer from American Airlines. Because of her long-time loyalty, she is
    eligible to obtain LIFETIME Platinum elite status on American if she
    fulfills a special “challenge”—flying 20,000 miles and 12 segments
    between October 1 and December 31. She covets the perks that come
    from Platinum status: priority check-in and boarding, lounge access, 100
    percent bonus on miles flown. The challenge is definitely doable; she has

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