The figure shows the volume index of a cake baked at 375 F, given the baking tim

Question

The figure shows the volume index of a cake baked at 375 F, given the baking time (in minutes) and the amount of leavening used (in grams). An index of 100 corresponds to the volume of the batter. No relative extreme points or saddle points lie outside the contour graph shown. cake volume index contours 35 T 33 E 3 29 leavening 3 3.3 3.7 4 4.3 47 5 grams. (a) Would a food scientist be more interested in finding a maximum or a minimum volume index? maximum minimum (b) Approximately where on the contour graph does the optimal point occur? leavening gm min baking time (c) Estimate the optimal value.

Explanation / Answer

(a)Food scientists would be interested in finding a maximum volume index as we can see from the figure that as we increase the volume index, baking time decreases which is desirable in food industry.also we can see that as the volume index is increased,leavening is increased upto a point and we know that optimum amount of leavening is desirable.
(b)Optimum point occures at the center of the elliptical contour i.e.
leavening= 4.2gm
Baking time=29min
(c)As distance between contours of 108.6 and 111 is less as compared to that of between 111 and 113.4 and distance between center of ellipse (optimum value) and 113.4 is further incresed so optimum value can be nearly taken as 117.
Maximum possible volume is 117 so it is 117% of volume of cake batter(100%)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.