A patient is to be given a mixture of two drugs Xeniccilin and Yasprin. Each of

Question

A patient is to be given a mixture of two drugs Xeniccilin and Yasprin. Each of these drugs causes the body temperature of the patient to change. When x milligrams of Xeniccilin and y milligrams of Yasprin are given the temperature of the patient is f(x,y) degrees farenheit. Suppose that initially the ptaient is given 30 mg of Xeniccilin and 20 mg of Yasprin and that this combination does not affect the patient's body temperature. (a) What is the practical significance of the facts that fx(30,20)=0.3 and fy(30,20)=0.6? (b) If the dosage of Xeniccilin is increased by a small amount, 1.3 milligrams, how much should the dosage of Yasprin be changed in order that the patient's temperature does not change? ITS NOT .866

Explanation / Answer

Initially the patient is given 30 mg of Xeniccilin and 20 mg of Yasprin so f(x,y) = f(30,20) and it does not change the temperature.

(a) fx(30,20) = 0.3 means that if the dosage of Xeniccilin is increased by 1 mg, then the temperature of patient will rise by 0.3 F.

fy(30,20) = - 0.6 means that if the dosage of Yasprin is increased by 1 mg, then the temperature of patient will fall by 0.6 F.

(b) Let the dosage of Yasprin to be changed in order that the patient's temperature does not change = y

Rise in temperature due to increased dosage of Xeniccilin (by 1.3 mg) = 1.3 * 0.3 = 0.39

Fall in temperature due to increased dosage of Yasprin ( by y mg) = 0.6y

0.6 y = 0.39

==> y = 0.65 mg

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