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An actor, Bob, wants to gain weight to look the part for his role as an overweight truck driver in an upcoming movie. He decides to add servings of banana splits (S) and bacon rolls (B) to his diet. Each serving of S is 1,000 calories and each serving of B is 500 calories. Bob has a history of health problems and his doctor has recommended that he needs to control his cholesterol and sugar levels in his food intake. Each serving of S contains 1 unit of cholesterol and 3 units of sugar. Each serving of B contains 4 units of cholesterol and 1 units of sugar. His doctor recommends that his cholesterol be no larger than 10 units and his sugar levels should be at least 2 units and no larger than 9 units. What should be the objective function (C) to select the optimal choice of Sand B in order for Bob to ingest as many calories as possible? A. C = 105 + 5B B. C = 1000S + 500B C. C = S+BD. None of the above

Sagot :

MrRoyal

Answer:

[tex]C = 1000S + 500B[/tex]

Step-by-step explanation:

Given

[tex]S = Banana\ Splits[/tex]

[tex]B=Bacon\ Rolls[/tex]

Reading through the question, we have:

Number of calories per serving:

[tex]S \to 1000[/tex]

[tex]B \to 500[/tex]

Let

[tex]x = Cholesterol[/tex]

[tex]y =Sugar[/tex]

So, we have:

Each serving of S

[tex]x \to 1S[/tex]

[tex]y \to 3S[/tex]

Each serving of B

[tex]x \to 4B[/tex]

[tex]y \to 1B[/tex]

Recommendation

[tex]x \to \le 10[/tex] - i.e. not more than 10 units of cholesterol

[tex]y \to \ge 2 \& \le 9[/tex] i.e. At least 2units but not more than 9 units of sugar

So, the constraints are:

[tex]S + 4B \le 10[/tex]

[tex]3S + B \ge 2[/tex]

[tex]3S + B \le 9[/tex]

Recall that the calories per serving is:

[tex]S \to 1000[/tex]

[tex]B \to 500[/tex]

Hence, the objective function is:

[tex]C = 1000S + 500B[/tex]

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