Leego needs to decide how many and what types of edible bricks to make for this...
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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 $3 per brick, rectangular bricks sell for the profit of $5 per brick, while circular bricks sell for a profit of $6 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 Sugar Butter 3 4 0.1 3 3 0.2 2 4 0.3 Leego has a total of 80 cups of flour, 120 cups of sugar, and 6 cups of butter to use. Also, they would like to make at least 2 square bricks. In order to maximize their profit, the senior Operations Manager at Leego has entered the following LP into Excel. 3r1 + 5x2 +6x3 maximize subject to 3r1 + 3x2+2rg 4x1 + 3x2 + 4x3 0.11 +0.22 +0.3r3 21 X1, X2, X3 <80 < 120 ≤ 6 > 2 20 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, print a copy of the Excel output. b. Suppose that the profit per square brick rises to $4. Will this change the optimal num ber of square bricks to make? c. How much would the price of rectangular bricks have to decrease before Leego decides to reduce the number of this kind of bricks to make? d. Suppose now that Leego is given an offer to buy 1 additional cup of butter at a price of $5. Should they accept this offer? Why or why not? If the answer is yes, then what will be the new optimal amounts of the three kinds of bricks? 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 $3 per brick, rectangular bricks sell for the profit of $5 per brick, while circular bricks sell for a profit of $6 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 Sugar Butter 3 4 0.1 3 3 0.2 2 4 0.3 Leego has a total of 80 cups of flour, 120 cups of sugar, and 6 cups of butter to use. Also, they would like to make at least 2 square bricks. In order to maximize their profit, the senior Operations Manager at Leego has entered the following LP into Excel. 3r1 + 5x2 +6x3 maximize subject to 3r1 + 3x2+2rg 4x1 + 3x2 + 4x3 0.11 +0.22 +0.3r3 21 X1, X2, X3 <80 < 120 ≤ 6 > 2 20 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, print a copy of the Excel output. b. Suppose that the profit per square brick rises to $4. Will this change the optimal num ber of square bricks to make? c. How much would the price of rectangular bricks have to decrease before Leego decides to reduce the number of this kind of bricks to make? d. Suppose now that Leego is given an offer to buy 1 additional cup of butter at a price of $5. Should they accept this offer? Why or why not? If the answer is yes, then what will be the new optimal amounts of the three kinds of bricks?
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