# Pokhara University||2015 Fall Business Mathematics ||

This is the question set along with answers of 2015 Fall Business Mathematics, which was taken by Pokhara University.

POKHARA UNIVERSITY

 Level:  Bachelor Semester – Fall Year: 2015 Programme: BBA/BBA-BI/ BBA-TT/BCIS/BHCM Full Marks: 100 Course: Business Mathematics Pass Marks: 45 Time:3hrs Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.

Section “A”

 Attempt all the questions. 10×2 1 Evaluate: 2 2 Find the interval on which the function is continuous. 2 3 Determine the function is increasing or decreasing at x = – 5. 2 4 Find if y = (- 5x2 + 3)3/2. 2 5 For f(x, y, z) =  xeyz  find at (2,  0,  3). 2 6 Find the elasticity of the demand function q at the given price level p = 3 for q = 2 7 If u = f(x, y) = x2y2 + XY is the utility function for first product x and second product y. Find the marginal utility of second product y. 2 8 A marginal revenue function is given by MR = 800 – 4x. Find the total revenue function if the revenue of 2 items is 2000. 2 9 Find the function  with the following property: f’(x) = + 5, f(9) = 0. 2 10 Draw a graph of the inequality: 2x + 3y 6 2

Section “B”

 Attempt any six questions 6×10 11 a)       Evaluate: . b)    A function g(x) is defined by g(x) = Find the value of k so that the function g(x) is continuous at x = 3 12 a)    A product with a large advertising budget has its sales are given by S = where t is the number of months the product has been on the market. i.          Find the rate of change of sales at any time t. ii.          What is the rate of change of sales at t=2? b) The demand function for a firm’s product is q = 150,000 – 75p where q equals the number of units demanded and p equals the price in dollars. i.          Determine the price which should be charged to maximize the total revenue. ii.        What is the maximum value for total revenue? 13 a)    Determine the locations and values of the absolute maximum for the function , where Prove that nd =  where AR is average revenue and MR is the marginal revenue. 14 a)    If U= x2y + y2z + z2x, then prove that = (x + y + z)2. b)    A manufacturer of two different types of drugs determines that its monthly revenues from the sale of x units of drug A and y units of drug B are given by dollars. i.          Find the rate at which revenues will increase with respect to the increase in sales of drug A at x = 4 units and y = 9 units. ii.          Find the rate at which revenues will increase with respect to the increase in sales of drug B at x = 4 units and y = 9 units. 15 a)    A sewing machine manufacturer sells its machine in two markets, foreign and domestic. It determines that the profit resulting from the sale of x machines in the domestic and y machines in the foreign market per week is .Find the number of machines that should be sold in the domestic and foreign markets per week in order to maximize profits. b)    Find x and y that maximize the utility function U = x2y2 subject to the budget construction   2x + 4y = 40. 16 Integrate any two of the following: a) b) c) 17 a)    Find the general and particular solution of the differential equation: = 3x + 5;  f ‘(2) = 4, f (–1) = 6. The demand function for a commodity is and the supply function is, find the consumer’s surplus at the equilibrium market price.

Section “C”

Case Analysis
18 Read the case situation below and answer the questions that follow.

Retailers often sell different brands of competing products. Depending on the joint demand for the products, the retailer may be able to set prices that regulate demand and, therefore, influence profits.

Suppose HOME-ALL, Inc., a national chain of home improvement retailers, sells two competing brands of interior flat paint, En-Dure 100 and Croyle& James, which the chain purchases for \$8 per gallon and \$10 per gallon, respectively. HOME-ALL’s research department has determined the following two monthly demand equations for these paints:

D = 120 – 40d + 20c and C = 680 + 30d – 40c

Where D is hundreds of gallons of En-Dure 100 demanded at \$d per gallon and C is hundreds of gallons of Croyle& James demanded at \$c per gallon. For what prices should HOME-ALL sell these paints in order to maximize its monthly profit on these items?

To answer this question, complete the following.

i) Recall that revenue is a product’s selling price per item the number of items sold. With this in mind, formulate HOME-ALL’s total revenue function for the two paints as a function of their prices.

ii) Form HOME-ALL’s profit function for the two paints (in terms of their selling prices).

iii) Determine the prices of each type of paint that will maximize HOME-ALL’s profit.

iv) Write a brief report to management that details your pricing recommendations and justifies them.

19

RMC Inc. is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 2/5 tons of material 1 and 3/5 of material 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3. After deducting relevant costs, the profit contribution is \$40 for every ton of fuel additive produced and \$30 for every ton of solvent base produced.

 Raw Material Amount Available for Production Material 1 20 tons Material 2 5 tons Material 3 21 tons

RMC’s production is constrained by the limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material:

Assuming that RMC is interested in maximizing the total profit contribution, answer the following:

i.          What is the linear programming model for this problem?

ii.          How many tons of each product should be produced, and what is the projected total profit contribution?

iii.          Is there any unused material? If so, how much?

iv.          Are any of the constraints redundant? If so, which ones?

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