Do a). Mr. Yara has 200 acres of land available to plant for three types of fruit trees (lemon, peach andcherry). Based on the market survey, lemon has a selling price of $2 per kg; peach has a sellingprice of $1.5 per kg and cherry has a selling price of $4 per kg. The average yield per acre forlemon, peach and cherry is 4, 6 and 2 tonne, respectively. The fertilizer requires per acre forlemon, peach and cherry is 100, 100 and 50 kg, respectively. An acre of lemon and cherryrequires 10 labour hours each whereas an acre of peach requires 12 labour hours. Maximumavailability of labour is 20,000 hours. The cost of fertilizer is $2 per kg and the cost of labour is$40 per hour. What is the optimal allocation of acre to the three types of fruit trees?[1 tonne = 1000kg](a) Formulate a linear programming model to maximize the profit.(b) Find the optimal solution by using simplex algorithm.(c) Regenerate the sensitivity report given below by using Excel's Solver.Variable CellsFinal Reduced Objective Allowable AllowableValue Cost Coefficient Increase DecreaseCellName$B$6 Value Lemon (x1)-920$C$6 Value Peach (x2)0$D$6 Value Cherry (x3)-820ConstraintsFinal ShadowConstraint Allowable AllowableIncrease DecreaseCellNameValuePriceR.H. Side$B$9 Land (acre) (LHS)8320$B$10 Labour (hour) (LHS)0(d) From the above sensitivity report, answer the following questions.(i) Interpret the reduced cost for the decision variable of cherry in terms of profitcontribution and optimal solution.(ii) Interpret the shadow prices for the land and labour constraints, respectively.(iii) Find the right hand side range for the labour constraint. Interpret the result about theshadow price, optimal solution and the value of the optimal solution.

Double check labour hour per acre. It looks not comparable with other details the question.

Answered: a) Formulate a linear programming model…

Math

Advanced Math

a) Formulate a linear programming model to maximize the profit.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 37E: Zaidah plans a raised flower bed 2 ft high by 12 ft wide by 15 ft long. The mulch, soil, and peat...

See similar textbooks

Related questions

Q: MCV4U 8.2.3 Assessment Check: Cartesian Equation of a Line Remember: Cartesian equation of a line in…

Q: . (D²+1)y= 10e²x When x = 0, y = 0, y' = 0

Q: Determine whether the argument is an example of inductive reasoning or deductive reasoning. Justify.…

A: Inductive reasoning: An inference which is based on an observation or a given sample is known as the…

Q: 4x-x² Given the rational function r(x)= x²-4 (a) Find all intercepts and asymptotes of r. (b)…

Q: iv. y = x² Plot A |Plot B Plot C No Match (b) For each of the direction fields shown below plot a…

Q: {₁,...,} is linearly independent if and only if {₁,...,} is an orthogonal set. True False

Q: 5. A = {0, 32, 62} where A-Z* 6. A = [5, 10-] where A = Z¹

Q: The following are the vertices of a triangle A(4, 0, -1), B(-4, -1, 0), and C(3, 1, 1), find: vector…

A: To find the given values:-

Q: Solve the following equations and compare the roots using the five methods. Tabulate the data…

A: Given: f(x)= x³ + 3x² - 2x - 7 To find: Solution

Q: 8 7 6 54 32 3 1 -4-3-2-1 + valuate f(2): (2) = olve f(x) = 2: 1 2 3 4 5

A: since horizontal axis represent x values and vertical axis represent f(x) values. so, from graph we…

Q: Miguel deposits ₱135,500 in a savings account that pay 13% interest converted semi-annually. If he…

Q: 1. Are the vectors (-3, 0, 4), (5, -1, 2) and (1, 1, 3) linearly dependent in R3? a. Yes b. No

Q: If n, k E Z. s. t. n is the square of an odd integer, then the perfect square of n must be of the…

Q: CLAMPED SPLINE MODEL PROBLEM = Suppose S(x) interpolates f(x) atxo = 0, x₁ 1 and 2 = 2 by a clamped…

Q: Simone got 3/4 of a full bar of chocolate. Hank was supposed to get 1/4 of the full chocolate bar,…

Q: 14a) 14b) f(x)= 2 4x-15 about the center x = 4 f(x) = ln(1+5x¹) about the center x = 0

Q: Solve the given homogeneous ODE. Also, state the value of a. 2xy + y² = 2x² a= dx

Q: The fox population in a certain region has an annual growth rate of 9 percent per year. It is…

A: Given: Annual Growth Rate: 9%

Q: 1. Evaluate the integral 2 4-x² 8x cos y y-4 by reversing the order of integration. dy dx

Q: . Define a relation on R²\{(0,0)} by letting (x₁, y₁)~(x₂,Y₂) if there exists a nonzero real number…

Q: In each of Problems 21 through 24, determine the values of r for which the given differential…

Q: 4. Let X an Y be sets with A, B C X and let f: X→Y be a function. Recall that {f(x) EYE A}, and…

Q: dy (x² + xy) = 3xy+2y² In solving , one sets y VX. Which one of the following equations are then…

Q: let P: XY be a function prove that Phas an inverse if and only if fis abijection.

A: Let us define a bijective functions. We know that , a function f : X → Y is bijective if it is both…

Q: The figure shows f, f', and f". Determine which is which. 2 y 0 -2 2

A: Solution :

Q: What is the order of the unique Lagrange inter- polating polynomial that passes through n + 1 data…

A: Solution

Q: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x-2ky + 5z = 0…

A: Given, plane1 =>kx+2y-2kz+3=0 and plane2 => x-2ky+5z=0

Q: Q3/ Compute the first three terms of the Taylor series method to obtain a solution = -xy correct to…

A: We have to solve the given problem by Taylor's method.

Q: 200 Let the functions f and g be differentiable at the inner point a of their domain. Then A] fg is…

Q: To what values does the Fourier sine series converge at z = =0, x= π/2, x = π, x = 3π/2, and z = 2π?

Q: High concentrations of carbon monoxide CO can cause coma and possible death. The time required for a…

A: Given: The time required for a person to reach a COHb level capable of causing a coma can be…

Q: dx 2. Evaluate _1 (1+x²³²) +√√1+x6 by Composite Simpson's 1/3 Rule.. n=4 I= (b − a): f(xo) +…

Q: Discuss the questions in groups. • What are some of the good and bad points about being a clown…

A: Since you posted multiple question, we will solve the first question for you. Kindly repost other…

Q: The operations manager of a mall order house purchases double (D) and twin (7) beds for resale. Each…

A: Let the weekly profit = Z Let number of double beds = x Let the number of twin beds = y So,…

Q: Suppose is the angle between u and 7. Then ||ū + v||² = ||ū||² + ||v||² +2||u||· ||v||· cos 0. True…

Q: y''(x) + (e^x)y'(x) + xy(x) = cos(x) Determine the particular solution up to terms of order O(x^5)…

A: Given DE is y''(x) + (e^x)y'(x) + xy(x) = cos(x) .....(1) We determine the particular solution up…

Q: Find the average rate of change of the function over the given interval. f(t) = 4t + 4, [1, 6]…

Q: 2. Find the mass of a lamina with density 8(x, y) = 3x, bounded by y = -x, y = 0 and x = √4-y².

A: Solution :

Q: Find the infimum, minimum, maximum and supremum of each of the following sets (write d.n.e. if it…

Q: What is the order of the unique Lagrange inter- polating polynomial that passes through n + 1 data…

Q: 3. Solve the following equations over the interval [0, 2π]. Use exact values where possible, or…

A: a) tan2x=13 tan2x=13tan x=±13x=π6,7π6,5π6,11π6

Q: What is the general form of the chosen low or- der polynomial model?

Q: Find the approximations TM and S, for n = 6 and 12. Then compute the corresponding errors ET, EM,…

A: n Tn Mn Sn 6 365.123457 243.850309 319.061728 12 304.486883 248.157311 284.274691 n ET…

Q: L²+R²x+²y=0 (Auxilary function)

A: Solution :

Q: Q4. (a) Let f(x) = 1 - 4x - 5x². (i) Express f(x) in the form p-q(x+r)2, hence or otherwise…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: 3. Emily is making a closed rectangular box with a square base from two different woods. The wood…

A: Given- Emily is making a closed rectangular box with a square base from two different woods. The…

Q: 12 Let (RTR) is topological Space Such that TR-243 U2GSR=R-G-G is finste} Find buz), Z², Z. z' then…

A: Here given ℝ, Tℝ is a topological space such that Tℝ=ϕ∪G⊂ℝ: ℝ-G=Gc is finite This topology is known…

Q: Q2/ Find the slope of the tangent to the curve at x = 8 y = 3x5 + 2√x + 4 + 4 + + 2³√√x+¹2+√5 3x²…

Q: Solve the following operation 42²³/7 V7 where Z=-4+50 Z=4+ 50 W = -2-6 č V = 2-i

A: To find- Solve the following operation 4z2w3v7 where z = -4 + 5i, w = -2 - 6i, v = 2 - i…

Q: Question 2 Demonstrate the solution of the following system using Gauss elimination with partial…

Question

Do a).

Mr. Yara has 200 acres of land available to plant for three types of fruit trees (lemon, peach and
cherry). Based on the market survey, lemon has a selling price of $2 per kg; peach has a selling
price of $1.5 per kg and cherry has a selling price of $4 per kg. The average yield per acre for
lemon, peach and cherry is 4, 6 and 2 tonne, respectively. The fertilizer requires per acre for
lemon, peach and cherry is 100, 100 and 50 kg, respectively. An acre of lemon and cherry
requires 10 labour hours each whereas an acre of peach requires 12 labour hours. Maximum
availability of labour is 20,000 hours. The cost of fertilizer is $2 per kg and the cost of labour is
$40 per hour. What is the optimal allocation of acre to the three types of fruit trees?
[1 tonne = 1000kg]
(a) Formulate a linear programming model to maximize the profit.
(b) Find the optimal solution by using simplex algorithm.
(c) Regenerate the sensitivity report given below by using Excel's Solver.
Variable Cells
Final Reduced Objective Allowable Allowable
Value Cost Coefficient Increase Decrease
Cell
Name
$B$6 Value Lemon (x1)
-920
$C$6 Value Peach (x2)
0
$D$6 Value Cherry (x3)
-820
Constraints
Final Shadow
Constraint Allowable Allowable
Increase Decrease
Cell
Name
Value
Price
R.H. Side
$B$9 Land (acre) (LHS)
8320
$B$10 Labour (hour) (LHS)
0
(d) From the above sensitivity report, answer the following questions.
(i) Interpret the reduced cost for the decision variable of cherry in terms of profit
contribution and optimal solution.
(ii) Interpret the shadow prices for the land and labour constraints, respectively.
(iii) Find the right hand side range for the labour constraint. Interpret the result about the
shadow price, optimal solution and the value of the optimal solution.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here