A farmer has land on which she plans to grow wheat and corn. Each acre of wheat requires 4 hoursof labor and $20 of capital, and each acre of corn requires 16 hours of labor and $40 of capital. Thefarmer has at most 800 hours of labor and $2400 of capital available. If the profit from an acre ofwheat is $80 and from an acre of corn is $100, how many acres of each crop should she plant tomaximize her profit?Let's finally answer the question. How many acres of wheat and corn should be planted? Fill inthe blanks (tip: all the answers should be whole numbers).The farmer should plantfor a maximum profit ofacres of wheat andacres of corn

A farmer has land on which she plans to grow wheat and corn. Each acre of wheat requires 4 hours of…

Answered: A farmer has land on which she plans to…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 24EQ: Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry...

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If during the following year it is predicted that each comedy skit will generate 30 thousand and each musical number 20 thousand, find the maximum income for the year. A television program director must schedule comedy skits and musical numbers for prime-time variety shows. Each comedy skit requires 2 hours of rehearsal time, costs 3000, and brings in 20,000 from the shows sponsors. Each musical number requires 1 hour of rehearsal time, costs 6000, and generates 12,000. If 250 hours are available for rehearsal and 600,000 is budgeted for comedy and music, how many segments of each type should be produced to maximize income? Find the maximum income.
Find the dimensions of a triangle whose width is four more than six times its height and has an area of 208 square inches.
Find the base and height of a triangle whose base is four inches more than six times height and hasan area of 456 square inches.
A farmer has 165 acres of land suitable for cultivating crops A and B. He has enough seeds available to plant 110 acres of crop A and 115 acres of crop B. Each acre of crop A requires 18 hours of labor, and each acre of crop B requires 19 hours of labor. The farmer has at most 3420 hours of labor available. He expects to make a profit of 130 dollars per acre on crop A and 190 dollars per acre on crop B. How many acres should the farmer plant in order to maximize his profit? acres of crop A, and acres of crop B.
A Toot can be made in 30 minutes and has a feather attached to it. A Wheet requires 15 minutes, has two feathers, and is sprinkled with 0.5 oz of sequin powder. A Honk requires 30 minutes, has three feathers, and one oz. of sequin powder. The net profit is $0.40 per Toot, $0.50 per Wheet, and $0.80 per Honk. The following resources are available: 80 hrs of labor, 360 feathers, and 90 oz. of sequin powder. Determine the quantity of each type of noisemaker that maximizes profit.
A tailor makes wool tweed sport coats and wool slacks. He is able to get a shipment of 150 square yards of wool cloth from Scotland each month to make coats and slacks, and he has 200 hours of his own labor to make them each month. A coat requires 3 square yards of wool and 10 hours to make, and a pair of slacks requires 5 square yards of wool and 4 hours to make. The tailor earns ₱50 in profit from each coat he makes and ₱40 from each pair of slacks. He wants to know how many coats and pairs of slacks to produce to maximize profit. Requirements: a) Define decision variables and tabulated data b) Formulate the Integer Linear Programming Model.
Suppose an accountant prepares tax returns for individuals and small businesses. Typically, each individual return requires 3 hours of her time and 1 hour of computer time. Each small business requires 4 hours of her time and 2 hours of computer time. Because of other business considerations, her time is limited to 240 hours and the computer time is limited to 100 hours. If she earns a profit of $80 on each individual return and a profit of $150 on each business return, how many returns of each type should she prepare to maximize her profit?
A bakery sells pies and cakes. Each pie costs $2 to produce, requires a half an hour of labor, and sells for $3; while each cake costs $3, requires an hour of labor, and sells for $5. How many pies and cakes, respectively, should be produced in each 8 hour day if the bakery spends no more than $30 per day on supplies?
A souvenir store wishes to produce two models of souvenirs: model A and model B. Every model-A souvenir will result to ₱14 profit, and every model-B souvenir will result to ₱23 profit. To manufacture a model-A souvenir requires 3 minutes on stage 1 and minutes on stage 2. A model-B souvenir requires 5 minutes on stage 1 and 4 minutes on stage 2, There are 270 minutes on stage 1 and 360 minutes on stage 2 for processing order. How many souvenirs of each model should the store make in order to maximize profit? Required: olve the linear programming model using simplex method.
A souvenir store wishes to produce two models of souvenirs: model A and model B. Every model-A souvenir will result to ₱14 profit, and every model-B souvenir will result to ₱23 profit. To manufacture a model-A souvenir requires 3 minutes on stage 1 and minutes on stage 2. A model-B souvenir requires 5 minutes on stage 1 and 4 minutes on stage 2, There are 270 minutes on stage 1 and 360 minutes on stage 2 for processing order. How many souvenirs of each model should the store make in order to maximize profit? Establish and solve the linear programming model using simplex method.

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