- Question 2 Real Juice A Manufacturer Of Diet Drinks Is Planning To Introduce A Special Drink That Will Magically Burn 1 (68.97 KiB) Viewed 99 times
QUESTION 2 Real-Juice, a manufacturer of diet drinks, is planning to introduce a special drink that will magically burn away fat. The drink is a bit expensive, but Real-Juice guarantees that a person using this diet plan will lose up to 50 pounds in just 3 weeks. The drink is made up of four "mystery" ingredients (ingredients A, B, C, and D). The plan calls for a person to consume at least three 12-ounce doses per day (ie. At least 36 ounces per day). Each of the four ingredients contains different levels of three chemical compounds (chemicals X, Y, and 2). Health regulations mandate that the dosage consumed per day should contain minimum prescribed levels of chemicals X and Y and should not exceed maximum prescribed levels for the third chemical, Z. The composition of the four ingredients in terms of the chemical compounds (units per ounce) is shown in table 2, along with the unit cost prices of the ingredients. Real-Juice wants to find the optimal way to mix the ingredients to create the drink, at minimum cost per daily dose. Chemical X Chemical Y Chemical Z COST PER OUNCE Ingredient A Ingredient B Ingredient 3 4 8 5 3 6 10 25 20 $0.40 $0.20 $0.60 Ingredient D 10 6 40 $0.30 Requirements At least 280 units At least 200 units At most 1,050 units REQUIRED: = a. Formulate a linear programming model for this problem. b. Solve this model by using the computer. c. State the optimal solution to the problem. d. What constraints are non-binding? e. Interpret the non-zero shadow prices in your output constraint table. f. Real-Juice can decrease the minimum requirements for chemical X by5 units, provided that the maximum limit allowed for chemical Z is reduced to 1000 units. Is this trade-off cost effective for Real-Juice to implement?