1. A major supermarket chain has decided to sub-contract production of ready-to-eat sandwiches to your production plant. Your plant can make three kinds of sand- wiches, each of which take the following amounts of raw ingredients (measured in grams) to produce: Sandwich Chicken Cheese Lettuce Tomato Bread 45 0 15 15 60 25 20 10 10 90 0 30 20 13 60 Chicken Salad Chicken Club Cheese and salad The total amount of time (measured in minutes) to make one of each sandwich is listed below, together with the price that the supermarket will pay to purchase one of each: Sandwich Time to Make Price 2.8 £1.25 4.8 £1.65 1.3 £0.95 Chicken Salad Chicken Club Cheese and Salad For the sake of this problem you can treat ingredients used and number of sandwiches made as continuous quantities we could perhaps think of this as the average made per day over a longer period, in which case making 100.43 sandwiches per day would still make sense. (a) Suppose that you have 5000g of chicken, 2500g of cheese, 1500g of lettuce, 6000g of bread, and 500g of tomato available from your supplier each day, and a total of 120 person-hours (= 7200 total minutes) of labour available each day. Write a linear program to find a production plan that maximises your daily revenue.
1. A major supermarket chain has decided to sub-contract production of ready-to-eat sandwiches to your production plant. Your plant can make three kinds of sand- wiches, each of which take the following amounts of raw ingredients (measured in grams) to produce: Sandwich Chicken Cheese Lettuce Tomato Bread 45 0 15 15 60 25 20 10 10 90 0 30 20 13 60 Chicken Salad Chicken Club Cheese and salad The total amount of time (measured in minutes) to make one of each sandwich is listed below, together with the price that the supermarket will pay to purchase one of each: Sandwich Time to Make Price 2.8 £1.25 4.8 £1.65 1.3 £0.95 Chicken Salad Chicken Club Cheese and Salad For the sake of this problem you can treat ingredients used and number of sandwiches made as continuous quantities we could perhaps think of this as the average made per day over a longer period, in which case making 100.43 sandwiches per day would still make sense. (a) Suppose that you have 5000g of chicken, 2500g of cheese, 1500g of lettuce, 6000g of bread, and 500g of tomato available from your supplier each day, and a total of 120 person-hours (= 7200 total minutes) of labour available each day. Write a linear program to find a production plan that maximises your daily revenue.
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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Transcribed Image Text:1. A major supermarket chain has decided to sub-contract production of ready-to-eat
sandwiches to your production plant. Your plant can make three kinds of sand-
wiches, each of which take the following amounts of raw ingredients (measured in
grams) to produce:
Sandwich Chicken Cheese Lettuce Tomato Bread
45
0
15
15
60
25
20
10
10
90
0
30
20
13
60
Chicken Salad
Chicken Club
Cheese and salad
The total amount of time (measured in minutes) to make one of each sandwich is
listed below, together with the price that the supermarket will pay to purchase one
of each:
Sandwich Time to Make
2.8
4.8
1.3
Chicken Salad
Chicken Club
Cheese and Salad
Price
£1.25
£1.65
£0.95
For the sake of this problem you can treat ingredients used and number of sandwiches
made as continuous quantities- -we could perhaps think of this as the average made
per day over a longer period, in which case making 100.43 sandwiches per day would
still make sense.
(a) Suppose that you have 5000g of chicken, 2500g of cheese, 1500g of lettuce,
6000g of bread, and 500g of tomato available from your supplier each day, and
a total of 120 person-hours (= 7200 total minutes) of labour available each day.
Write a linear program to find a production plan that maximises your daily
revenue.
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