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A company manufactures two products. The price hnction for product A tr。-18-1 x both in thousands...
A company manufactures two products. The price function for product A is p = 19 − 1 2 x (for 0 ≤ x ≤ 38), and fo...
A company manufactures two
products. The price function for product A is
p = 19 −
1
2
x
(for 0 ≤ x ≤ 38),
and for product B is
q = 33 − y
(for 0 ≤ y ≤ 33),
both in thousands of dollars, where x and y
are the amounts of products A and B, respectively. If the cost
function is
C(x, y) = 11x + 17y − xy + 7
thousands of dollars, find the quantities...
Research shows that the demand function for a new product is d(x)=-5 x+18
Research shows that the demand function for a new product is d(x)=-5 x+18, where x represents the number of items in thousands and d represents the item price in $.The cost function is C(x)=2 x+9.a. State the Revenue function R(x) [1 mark]b. Find the corresponding Profit function P(x). [1 mark]c. How many items must be sold to maximize profit? [2 marks]c. How many items must be sold for the company to break even? [2 marks] Hint: R(x)=x · p(x). The...
SHOW ALL YOUR WORK AND WRITE DOWN VERY NEATLY 2. The revenue R, in thousands of dollars, from producing and selling σ hundred LCD TVs is given by R(a)--5z? + 35a2 + 155z for 0 < π < 10.07 a. Us...
SHOW ALL YOUR WORK AND WRITE DOWN VERY NEATLY
2. The revenue R, in thousands of dollars, from producing and selling σ hundred LCD TVs is given by R(a)--5z? + 35a2 + 155z for 0 < π < 10.07 a. Use a graphing utility to graph y - R(r) and determine the number of TVs which should be sold to maximize revenue. What is the maximum revenue? Why does this amount produce maximum revenue? b. Assume that the cost, in...
1+1 5. [10 marks) Find all values of k such that f(x) = -r2 + 2kr...
1+1 5. [10 marks) Find all values of k such that f(x) = -r2 + 2kr +1" has domain (-0,0). 6. [10 marks] Sketch the graph of y = -2 -2 log: (2-2) and find its domain, range, -intercept and y-intercept. Show your transformations step by step. 7. (12 marks] (a) [8 marks) Find the equation of the tangent line to the graph of the function f(x) = 3.0" - 6x2 - 7 at = 2 (b) (4 marks) Find...
The revenue and cost functions for a particular product are given below.
The revenue and cost functions for a particular product are given below. The cost and revenue are given in dollars, and x represents the number of unitsR(x)=-0.8x2+608xC(x)=256x+36720(a) How many items must be sold to maximize the revenue?(b) What is the maximum revenue?(c) Find the profit function.(d) How many items must be sold to maximize the profit?(e) What is the maximum profit?(f) At what production level(s) will the company break even on this product?
The following information is provided for two products: Product X Product Y Selling price per unit...
The following information is provided for two products: Product X Product Y Selling price per unit $35 $25 Variable cost per unit 20 15 Assume the products will be sold in a store where shelf space is a scarce resource and there is sufficient room for only one of the two products. Expected sales for Product X are 6,000 units, and expected sales for Product Y are 8,000 units. Which product should be sold and why? A) Product Y should...
A company produces two types of solar panels per year: x thousand of type A and...
A company produces two types of solar panels per year: x thousand of type A and y thousand of type B. The revenue and cost equations, in millions of dollars, for the year are given as follows. R(x,y)=3x+5y C(x,y)=x^2− 4xy + 9y^2 + 7x - 43y - 9 Determine how many of each type of solar panel should be produced per year to maximize profit.
Farris Company reported the following information for its two products: Product X Product Y Selling price...
Farris Company reported the following information for its two products: Product X Product Y Selling price per unit $ 110 $ 120 Variable cost per unit 66 54 Due to labor constraints, demand for each of the products is greater than its supply. Product X requires one hour of labor to produce and product Y requires three hours of labor to produce. Which of the following statements is true? Product X should be produced and sold because it has a...
A company wants to determine how many units of each of two products, A and B,...
A company wants to determine how many units of each of two products, A and B, they should produce. The profit on product A is $50 and the profit on product B is $45. Applying linear programming to this problem, which of the following is the objective function if the firm wants to make as much money as possible? Maximize Z = A/45B + B/50A Minimize Z = 50 A + 45 B Maximize Z = A + B Minimize...
A company manufactures four products (1,2,3,4) on two machines (X and Y). The time (in minutes)...
A company manufactures four products (1,2,3,4) on two machines (X and Y). The time (in minutes) to process one unit of each product on each machine is shown below:, Product 1 in X = 10 min , in Y= 27 min Product 2 in X = 12 min , in Y =19 min Product 3 in X =13 min,in Y =33 min Product 4 in X = 8 min,in Y =23 min The profit per unit for each product (1,2,3,4)...
A company manufactures two
products. The price function for product A is
p = 19 −
1
2
x
(for 0 ≤ x ≤ 38),
and for product B is
q = 33 − y
(for 0 ≤ y ≤ 33),
both in thousands of dollars, where x and y
are the amounts of products A and B, respectively. If the cost
function is
C(x, y) = 11x + 17y − xy + 7
thousands of dollars, find the quantities...
Research shows that the demand function for a new product is d(x)=-5 x+18, where x represents the number of items in thousands and d represents the item price in $.The cost function is C(x)=2 x+9.a. State the Revenue function R(x) [1 mark]b. Find the corresponding Profit function P(x). [1 mark]c. How many items must be sold to maximize profit? [2 marks]c. How many items must be sold for the company to break even? [2 marks] Hint: R(x)=x · p(x). The...
SHOW ALL YOUR WORK AND WRITE DOWN VERY NEATLY
2. The revenue R, in thousands of dollars, from producing and selling σ hundred LCD TVs is given by R(a)--5z? + 35a2 + 155z for 0 < π < 10.07 a. Use a graphing utility to graph y - R(r) and determine the number of TVs which should be sold to maximize revenue. What is the maximum revenue? Why does this amount produce maximum revenue? b. Assume that the cost, in...
1+1 5. [10 marks) Find all values of k such that f(x) = -r2 + 2kr +1" has domain (-0,0). 6. [10 marks] Sketch the graph of y = -2 -2 log: (2-2) and find its domain, range, -intercept and y-intercept. Show your transformations step by step. 7. (12 marks] (a) [8 marks) Find the equation of the tangent line to the graph of the function f(x) = 3.0" - 6x2 - 7 at = 2 (b) (4 marks) Find...
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