1. A company produces two colors of cloth, namely red and pink. In order to produce thesecolors, 2 special raw materials are being used by the company. The production data isgiven below:Meters of raw material per meter ofMaximumdailyavailabilityRed ClothPink ClothRaw Material 1216Raw Material 2424Profit per ton (1000)According to the dealer, the daily maximum demand for red cloth is 2 meters andthe daily demand for red cloth can't exceed that for pink cloth by more than 1 meter. Thecompany wants to maximize its daily profit.a. Construct the LP Model of this problem.b. Find the optimal solution using Graphs. (graphing paper or desmos)c. Find the optimal solution using Excel Solver. (Sheet 1)d. Find the optimal solution using Algebraic Solution.e. Find the optimal solution using the Simplex Method. (Not in excel)

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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34. Due to the rising demand for face masks, a manufacturer decides to target a daily profit of PhP 1,000,000.00. If P(x) = 2r+ x- 10 represents average total daily cost at x assumed at PhP 500.00, what is the difference between the daily target profit and average total daily cost? B. PhP 420, 510.00 C. PhP 499,510.00 A. PhP 399, 520.00 105.00 D. PhP 599,
The demand function for a good is given by the equation P = a − bQ while the totalcost function is TC = dQ^2 + eQ + f, where a, b, d, e and f are positive constants.(a) Derive the equation for profit.(b) Derive an expression for the value of Q for which profit is maximized.
Q1) A retail. Store stocks two types of shirts A and B. These are packed in attractive cardboard boxes. During a week the store can sell a maximum of 400 shirts of type A and a maximum of 300 shirts of type B. The storage capacity, however, is limited to a maximum of 600 of both types combined. Type A shirt fetches a profit of SR 2/- per unit and type B a profit of SR. 5/- per unit. (a) Formulate a mathematical model of the problem.
The Metropolitan Tiles Company manufactures two types of floor tiles using the same production process. The product transformation curve for the input used per week is defined by the function : y - 300/(x-30) = 15 , (x<30) Question (a) Find the largest amount of each type that can be produced per week. a. x=100 tiles; y=500 tiles b. x=1000 tiles; y=5000 tiles c. x=1000 tiles; y=500 tiles
17. A manufacturer can sell a certain health supplement for P1,100 per unit. Its total cost consists of a fixed overhead of Php75,000 plus production costs of Php440 per unit. b)What is the manufacturer's profit or loss if 100 units are sold? P(x) =R(x)- C(x) =660x - 75,000 P(100) =660(100) - 75,000 == - 9,000 This is a loss of Php9,000.
what is the production level that minimizes the marginal cost?
3.) The revenue equation (in billions of dollars) for corn production in the United States is approximated by R(x)=0.016x² +1.034x+11.338 Where x is in billions of bushels. For example if you have 10 billion bushels, then x = 10. (Data from www.usda.gov) a.) Find the marginal revenue function b.) Find and interpret the marginal revenue for 15 billion bushels c.) Find and interpret the marginal revenue for 20 billion bushels
Suppose the Supply function for a product is given as p=30+ 0.001x^2 and the Demand function is given as p= 90-0.3x . Sketch the graph of the two functions, for 0 ≤ x ≤ 300. Make sure to LABEL your x and y axes with their scales. Find the point of intersection between the two functions. You do not need to do this algebraically. Find the Consumer’s Surplus using calculus.
If the demand function for a commodity is given by the equation p^2 + 4q = 2800 and the supply function is given by the equation 1000 − p^2 + 2q = 0, find the equilibrium quantity and equilibrium price

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