Using excel solve this Leego needs to decide how many and what types of edible bricks to make for this week. They make three kinds of edible bricks (based on their shapes): square, rectangular, and circular. Square bricks sell for a profit of $5 per brick, rectangular bricks sell for the profit of $4 per brick, while circular bricks sell for a profit of $2 per brick.
There are three main items required to make these edible bricks: flour, sugar, and butter. The number of cups of each ingredient needed to make each kind of bricks are given in the chart below. Leego has a total of 50 cups of flour, 120 cups of sugar, and 4 cups of butter to use. To maximize their profit, the senior Operations Manager at Leego has entered the following LP into Excel.
maximize 5x1 + 4x2 + 2x3
subject to
4x1 + 3x2 + 1x3 <= 50
2x1 + 1x2 + 4x3 <= 120
0.3x1 + 0.2x2 + 0.1x3 <= 4
x1, x2, x3 >= 0
Solve the above LP using Excel and answer the following questions.
a. What is the optimal number of each kind of edible bricks (fractions are allowed if necessary)? What is the maximum possible profit that Leego can obtain? Please include a screenshot of the Excel sheet with the formulation, as well as the sensitivity report.
b. Suppose that the profit per square brick rises to $6. Should Leego change the number of square bricks they produce?
c. Suppose now that Leego is given an offer to buy an additional quarter cup (0.25 cups) of butter at a price of $2. Should they accept this offer? Why or why not?
2. Leego needs to decide how many and what types of edible bricks to make for this week. They make three kinds of edible bricks (based on their shapes): square, rectangular, and circular. Square bricks sell for a profit of $5 per brick, rectangular bricks sell for the profit of $4 per brick, while circular bricks sell for a profit of $2 per brick.
There are three main items required to make these edible bricks: flour, sugar, and butter. The number of cups of each ingredient needed to make each kind of bricks are given in the chart below.
Ingredient Square brick Rectangular brick Circular brick
Flour 4 3 1
Sugar 2 1 4
Butter 0.3 0.2 0.1
Leego has a total of 50 cups of flour, 120 cups of sugar, and 4 cups of butter to use. To maximize their profit, the senior Operations Manager at Leego has entered the following LP into Excel.
maximize 5x1 + 4x2 + 2x3
subject to
4x1 + 3x2 + 1x3 <= 50
2x1 + 1x2 + 4x3 <= 120
0.3x1 + 0.2x2 + 0.1x3 <= 4
x1, x2, x3 >= 0
Solve the above LP using Excel and answer the following questions.
a. What is the optimal number of each kind of edible bricks (fractions are allowed if necessary)? What is the maximum possible profit that Leego can obtain? Please include a screenshot of the Excel sheet with the formulation, as well as the sensitivity report.
b. Suppose that the profit per square brick rises to $6. Should Leego change the number of square bricks they produce?
c. Suppose now that Leego is given an offer to buy an additional quarter cup (0.25 cups) of butter at a price of $2. Should they accept this offer? Why or why not?
