A company makes two types of machines, type A and type B. The profit, P (in dollars), of producing x machines of type A and y machines of type B per day is P(x, y) = 80x + 100y - x^2 - y^2 - xy How many machines of each type should be manufactured and sold each day to maximize profit? What is the maximum profit?
Added by Paula C.
Close
Step 1
Step 1: Take the partial derivative of the profit function with respect to x: \[ \frac{\partial P}{\partial x} = 80 - 2x - y \] Show more…
Show all steps
Your feedback will help us improve your experience
Vishal Parmar and 76 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A firm produces two types of earphones per year: $x$ thousand of type $A$ and $y$ thousand of type $B$. If the revenue and cost equations for the year are (in millions of dollars) $$ \begin{array}{l} R(x, y)=2 x+3 y \\ C(x, y)=x^{2}-2 x y+2 y^{2}+6 x-9 y+5 \end{array} $$ determine how many of each type of earphone should be produced per year to maximize profit. What is the maximum profit?
Multivariable Calculus
Maxima and Minima
Shop manufactures two types of bolts on three groups of machines. The time required on each group differs, as shown in the following table. (TABLE CAN'T COPY) In a day, there are $240,720,$ and 160 minutes available, respectively, on these machines. Type A bolts sell for $10 \&$ and Type B bolts for $12 \notin .$ How many of each type of bolt should be manufactured per day to maximize revenue? What is the maximum revenue?
Systems and Matrices
Systems of Inequalities and Linear Programming
Maximum profit: A kitchen appliance manufacturer can produce up to 200 appliances perday. The profit made from the sale of these machines can be modeled by the function $P(x)=-0.5 x^{2}+175 x-3300,$ where $P(x)$ is the profit in dollars, and $x$ is the number of appliances made and sold. Based on this model, a. Find the $y$ -intercept and explain what it means in this context. b. Find the $x$ -intercepts and explain what they mean in this context. c. Determine the domain of the function and explain its significance. d. How many should be sold to maximize profit? What is the maximum profit?
Polynomial and Rational Functions
Quadratic Functions and Applications
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD