MX4086 Optimisation Theory-Programming Problem

Task:

1.A manufacturer of a dried fruit production company has 140 pounds of dried cherries and 170 pounds of golden raisings in stock. He decides to sell them in the form of two different mixtures. One mixture will contain one-half of dried cherries and one-fourth of golden raisings by weight and will sell for $2.25 per pound.

The other mixture will contain one-half of dried cherries and two-thirds golden raisings by weight and will sell for $1.75 per pound.

How many pounds of each mixture should the manufacturer prepare to maximize his sales revenue?

Formulate a linear programming problem model for the problem and then solve it using Matlab.

2. The SaveWaste city recycling facility runs two recycling centers within the city limits. Center 1 costs $40 to run for an eight-hour day.

On a typical day, 140 pounds of glass and 60 pounds of aluminum are deposited at Center 1. Center 2 costs $50 for an eight-hour day, with 100 pounds of glass and 180 pounds of aluminum deposited per day.

The Save Waste city commits to deliver at least 1540 pounds of glass and 1440 pounds of aluminum per week to both centers.

How many days per week should the city open each center to minimize its cost and still meet the city’s recycling needs? Formulate a linear programming problem model for the problem and then solve it using Matlab.

3. Suppose that your community club is planning to make greeting cards, candy bags, and knitted toys to sell at the winter festival during a fundraiser event.

The community club divide into three groups – the first group decides to make greeting cards, the second group plans to make cookies.

The third group with individuals that are good at knitting plans to make knitted toys. Considering the number of people available and time constraints due to work and other family commitments, only 100 candy bags, and 60 knitted toys can be made each week but can made 75 or more greeting cards.

4. Enough material is delivered to the community center every Monday morning to make a total of 200 items per week. Because the material is being donated by community members, each greeting card sold makes a profit of $1 and each candy bag makes a profit of $3, and finally knitted toys make a profit of $2.

To make the most money from the fundraiser, how many of each item should be made each week? Formulate a linear programming problem model for the problem and then solve it using Matlab.