Business Mathematics BA/AD/BS/B.ED AIOU — Allama Iqbal Open University 2023

ALLAMA IQBAL OPEN UNIVERSITY ISLAMABAD Level: BA/AD/BS/B.Ed Semester: Autumn 2023 Subject/Course Code: Business Mathematics (1429) Maximum Marks: 100 Maximum Time: 03 Hours Pass Marks: BA 40, AD/BS/B.Ed 50 Medium of Instructions: English NOTE: Attempt any FIVE questions Q.No. Questions Marks 1. a) A patient in a hospital is required to have at least 84 units of drug A and 120 units of drug B each day (assume that an over dosage of either drug is harmless). Each gram of substance M contains 10 units of drug A and 8 units of drug B, and each gram of substance N contains 2 units of drug A and 4 units of drug B. How many grams of substances M and N can be mixed to meet the minimum daily requirements? 10+10 b) Solve: |7x - 12| = |4 - 3x| 2. The annual profit for a firm depends upon the number of units produced. Specifically, the function which describes the relationship between profit P (Stated in dollars) and the number of units produced x is P = -0.01x^2 + 5,000x - 25,000 (i) Determine the number of units x which will result in maximum profit. (ii) What is the expected maximum profit? 20 3. Solve graphically and check your answer algebraically. -x + 3y = 2 4x - 12 = -8 20 4. Find A^-1 and show that AA^-1 = I, if A = [2 3 0; 1 2 3; -8 5 -5] 20 5. Determine the location and values of the absolute maximum and absolute minimum for the given function: f(x) = (-6x + 7)^4, where 0 <= x <= 3 20 6. Find f(x), f'(x), f''(x), f'(1), f''(1), f'(5) and f''(5) when f(x) = 2x / (x^2 + 1) 20 7. For a given function f(x) = x^4 + x^2 + 10 (i) find those open intervals over which the function is concave up, concave down. (ii) find all points of inflection. 10+10 8. Define critical point, point of inflection. Find all relative extrema, using First Derivative Test. Sketch a graph of the function. f(x) = x^2 / (x - 1) 20