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A grocery store manager must decide how to best present a limited supply of popcorn and soda to its customers.  Popcorn can be sold by itself for a profit of $1.35 per tin.  Soda can likewise be sold at a profit of $2.45 per liter.  To increase appeal to customers, one tin of popcorn and a liter of soda can be packaged together and sold for a profit of $3.15 per bundle.  The manager has at most 115 tins of popcorn and 145 liters of soda to make available each day.  The manager has decided to stock at least 80 individual tins of popcorn per day (excluding popcorn bundled with soda).  Demand for individual liters is at most 135 liters per day (excluding soda bundled with popcorn).  The manager wishes to determine how much of each product to stock each day. What is the maximum daily profit that the grocery store can achieve.  (Let P be the number of individual tins of popcorn stocked each day.  Let S be the number of individual sodas stocked each.  Let B be the number of bundles stocked.  Assume that, within the limitations established by the constraints, the store can sell all the products it stocks.)

A grocery store manager must decide how to best present a limited supply of popcorn and soda to its customers.  Popcorn can be sold by itself for a profit of $1.35 per tin.  Soda can likewise be sold at a profit of $2.45 per liter.  To increase appeal to customers, one tin of popcorn and a liter of soda can be packaged together and sold for a profit of $3.15 per bundle.  The manager has at most 115 tins of popcorn and 145 liters of soda to make available each day.  The manager has decided to stock at least 80 individual tins of popcorn per day (excluding popcorn bundled with soda).  Demand for individual liters is at most 135 liters per day (excluding soda bundled with popcorn).  The manager wishes to determine how much of each product to stock each day. What is the maximum daily profit that the grocery store can achieve.  (Let P be the number of individual tins of popcorn stocked each day.  Let S be the number of individual sodas stocked each.  Let B be the number of bundles stocked.  Assume that, within the limitations established by the constraints, the store can sell all the products it stocks.)

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 93P
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A grocery store manager must decide how to best present a limited supply of popcorn and soda to its customers.  Popcorn can be sold by itself for a profit of $1.35 per tin.  Soda can likewise be sold at a profit of $2.45 per liter.  To increase appeal to customers, one tin of popcorn and a liter of soda can be packaged together and sold for a profit of $3.15 per bundle.  The manager has at most 115 tins of popcorn and 145 liters of soda to make available each day.  The manager has decided to stock at least 80 individual tins of popcorn per day (excluding popcorn bundled with soda).  Demand for individual liters is at most 135 liters per day (excluding soda bundled with popcorn).  The manager wishes to determine how much of each product to stock each day.

What is the maximum daily profit that the grocery store can achieve.  (Let P be the number of individual tins of popcorn stocked each day.  Let S be the number of individual sodas stocked each.  Let B be the number of bundles stocked.  Assume that, within the limitations established by the constraints, the store can sell all the products it stocks.)

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