Recall from Exercise 47 of Section 7.1 that an empirical formula for the surface area of a person’s body is S(W, H) = 0.0072W^0.425 H^0.725 where W (kg) is the person’s weight and H(cm) is his or her height. Suppose for a short period of time, Maria’s weight adjusts as she grows taller so that W + H = 160. With this constraint, what height and weight will maximize the surface area of Maria’s body?

Data from Exercise 47 of Section 7.1

Pediatricians and medical researchers sometimes use the following empirical formula* relating the surface area S (m²) of a person to the person’s weight W (kg) and height H (cm):

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S(W, H)= 0.0072 W0.425H0.725