A 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 $0.05 foreach salad ordered. The price of a turkey plate is $12.00 minus $0.01 multiplied by the square of the number of turkey platesordered. Guests pay for their meal only after everyone has placed their orderUsing 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: $

Question
Asked Nov 18, 2019
16 views

The answer I keep getting is $17.04 but I keep being told the answer is wrong. I've managed to figure out that the value where the function is at its max is 97.5 and since $17.04 isnt the answer I'm totally confused as to what it is.

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 $0.05 for
each salad ordered. The price of a turkey plate is $12.00 minus $0.01 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: $
help_outline

Image Transcriptionclose

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 $0.05 for each salad ordered. The price of a turkey plate is $12.00 minus $0.01 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: $

fullscreen
check_circle

Expert Answer

Step 1
help_outline

Image Transcriptionclose

Let x be the number of sold dishes and the price of the salad is S = 10-0.05 Then, 100-xis the number of sold turkey and price ofthe turkey is s 12-0.01(100-x) The Revenue function is R(x)x(10-0.05x) (100-x)(12-0.01(100-x))

fullscreen
Step 2
help_outline

Image Transcriptionclose

Differentiate the revenue function with respect to x. dR d (x(10-0.05x)+(100-x)(12-0.01(100-x) dc (10-0.05(2x))+12-0.01(100-x))(100-x) d (12-0.01(100-x)) dx +(100 x) (10-0.05(2x))+(12-0.01(100-x))(-1) +(100-x(0-(0.01)(2)(100-x)(-1)} 10-0.01x-12+ 0.1(100- x)0.02(100-x)(100-:x)

fullscreen
Step 3
help_outline

Image Transcriptionclose

Equate the first derivative to zero to find the maximum. 10-0.01r -12 0.1(100-x)+0.02(100-x)(100-x)=0 0.12.x2-24.01x +1198 = 0 2401-14401 2401-14401 24 24 x -105.0418,x=95.0415 Since the root x = 105.0418 is greater than total orders, ignore the root x 105.0418 The number of sold dishes is 95 and the number of sold turkey is 100-95=5.

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Related Calculus Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: A particle moves along the curve below.  y=(24+(x^3))^(1/2) As it reaches the point (1,5), the y-coo...

A: A particle moves along the curve f(x). As it reaches the point (1,5), the y-coordinate is increasing...

question_answer

Q: find the limit. use l'Hospital's rule where appropriate.

A: Refer to the question we need to find the limit of the following expression

question_answer

Q: If k is a positive integer, find the radius of convergence, R, of the series the sum from n=0 to inf...

A: Given:

question_answer

Q: Find the derivative matrix for the functions at the given points. Then find f o k; (s0,t0)=(1,1). a)...

A: Let us first write the definition of the derivative matrix for the functions at the given points.

question_answer

Q: sin(7x 2) dx cos2 (7x 2)

A: Let u=cos(7x+2)differentiate both sides w.r.t. x.Use chain rule for cos(7x+2)From there we get du/-7...

question_answer

Q: A builder intends to construct a storage shed having a volume of 900 cubic feet. and flat roof, and ...

A: According to the given information:Volume of storage shed = 900 cubic feet Width = 2/3 of the length...

question_answer

Q: Exercise 7: Let a < b. Suppose that f and g are two functions that are continuous on [a, bl, and dif...

A: Let a &lt; b. Suppose that f and g are two functions that are continuous on [a, b], and differentiab...

question_answer

Q: Set up, but do not evaluate the integral for the length of the curve.

A: We know that length of curve y=f(x) from x=a to x=b is given by

question_answer

Q: Evaluate the indefinite integral. ∫cos(2x)(9−sin(2x))^(1/2)dx

A: Given: