Attempt 3>Question 1 of 18A food truck caters an event attended by 100 guests. Every guest orders one of two possible dishes: a salad or a turkey plateThe price of each meal decreases as more of that particular type are ordered. The price of a salad is $10.00 minus $0.04 foreach salad ordered. The price of a turkey plate is $12.00 minus $0.02 multiplied by the square of the number of turkey platesordered. Guests pay for their meal only after everyone has placed their order.Using differentiation, find the maximum revenue for the food truck.Remember that the number of meals is a positive integer. Round revenue to the nearest centmaximum revenue: $

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Asked Nov 14, 2019
Attempt 3
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Question 1 of 18
A food truck caters an event attended by 100 guests. Every guest orders one of two possible dishes: a salad or a turkey plate
The price of each meal decreases as more of that particular type are ordered. The price of a salad is $10.00 minus $0.04 for
each salad ordered. The price of a turkey plate is $12.00 minus $0.02 multiplied by the square of the number of turkey plates
ordered. Guests pay for their meal only after everyone has placed their order.
Using differentiation, find the maximum revenue for the food truck.
Remember that the number of meals is a positive integer. Round revenue to the nearest cent
maximum revenue: $
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Attempt 3 > Question 1 of 18 A food truck caters an event attended by 100 guests. Every guest orders one of two possible dishes: a salad or a turkey plate The price of each meal decreases as more of that particular type are ordered. The price of a salad is $10.00 minus $0.04 for each salad ordered. The price of a turkey plate is $12.00 minus $0.02 multiplied by the square of the number of turkey plates ordered. Guests pay for their meal only after everyone has placed their order. Using differentiation, find the maximum revenue for the food truck. Remember that the number of meals is a positive integer. Round revenue to the nearest cent maximum revenue: $

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Expert Answer

Step 1

Let x guests ordered salad then (100-x) guests ordered turkey plate.

Now, since, the price of a salad is $10 minus $0.04 for each salad ordered,

So, we have

y1 = 10-0.04x

And now, the price of a turkey plate is $12 minus $0.02 multiplied by the square of the number of turkey plates ordered,

So, we have

y2 = 12-0.02(100-x)2

Therefore, total revenue is given by:

10-0.04x+12-0.02 (100-x)
22-0.04x-0.02(10000+x2 - 200x)
=-0.02x23.96x-178
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10-0.04x+12-0.02 (100-x) 22-0.04x-0.02(10000+x2 - 200x) =-0.02x23.96x-178

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Step 2

Now, differentiate with respect to x and put equal to zero to find the critical point:

y'=-0.04x3.96
Now
y'= 0
-0.04x+3.96 = 0
x = 99
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y'=-0.04x3.96 Now y'= 0 -0.04x+3.96 = 0 x = 99

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Step 3

Now, find second deriv...

y"=-0.04
Now
y "(99)=-0.04 < 0
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y"=-0.04 Now y "(99)=-0.04 < 0

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