1. BUSINESS MATHEMATICS & STATISTICS

2. SETTING UP LINEAR EQUATIONS Zain purchases the same amount of commodity 1 and 2 each week After price increases from Rs. 1.10 to Rs. 1.15 per item of commodity 1, and from Rs. 0.98 to Rs. 1.14 per item of commodity 2, the weekly bill rose from Rs. 84.40 to Rs. 91.70. How many items of commodity 1 and 2 are purchased each week?

3. SETTING UP LINEAR EQUATIONS Let x = # of commodity 1 Let y = # of commodity 2 1.10x +0.98y= 84.40 1.15x+1.14y=91.7 Eliminate x by Dividing by 1.10 Eliminate x by Dividing by 1.15

4. SETTING UP LINEAR EQUATIONS x + 0.8909y = 76.73 x + 0.9913y = 79.74 Subtract.1004y = 3.01 y=29.98 i.e. 30 nos. 1.10x + 0.98y = 84.40 Substitute value of y 1.10x + 0.98(29.98) = 84.40 1.10x + 29.38 = 84.40 1.10x = 84.40 - 29.38 1.10x = 55.02 x = 50.02 i.e. 50 nos.

5. SETTING UP LINEAR EQUATIONS Equation 1 1.10x + 0.98y = 84.40 (1.10x + 0.98y)/1.10 = 84.40/1.10 x + 0.8909y = 76.73 Equation 2 1.15x + 1.14y = 91.70 (1.15x + 1.14y)/1.15 = 91.70/1.15 x + 0.9913y = 79.74

6. SETTING UP LINEAR EQUATIONS New weekly cost Commodity 1: 50 x 1.15 = 57.50 Commodity 2: 30 x 1.14 = 34.20 Total cost = 91.70

7. TERMINOLOGY Business Costs Or Expenses Fixed Costs Do not change if sales increase or decrease e.g. rent, property taxes, some forms of depreciation Variable Costs Do change in direct proportion to sales volume e.g. material costs, direct labour costs

8. TERMINOLOGY Break Even Point A point at which Neither a profit nor loss is made

9. TERMINOLOGY Contribution Margin is the Rs. amount that is found by deducting ALL Variable Costs from Net Sales and ‘contributes’ to meeting Fixed Costs and making a ‘Net Profit’ Contribution Rate is the Rs. amount expressed as a percent (%) of Net Sales

10. TERMINOLOGY A Contribution Margin Statement Rs. % Net Sales(Price * # Units Sold) x 100 Less: Variable Costs x x Contribution Margin x x Less: Fixed Costs x x Net Income x x

11. Scenario 1 Market research for a new product indicates that the product can be sold at Rs. 50 per unit. Cost analysis provides the following information: Fixed Costs per period = Rs. 8640 Variable Costs = Rs. 30 per unit. Production Capacity per period = 900 units How much does the sale of an additional unit of a firm’s product contribute towards increasing its net income?

12. Scenario 1 Contribution Margin = CM = S – VC Contribution Rate = CR = CM/S * 100% *Break Even Point:...in Units (x) : Rs. x = (FC / CM)* S...in Sales Rs. : Rs. x = (FC / CM)* S...in % of Capacity : BEPin Units/PC*100 * At Break Even, Net Profit or Loss = 0

13. Scenario 1 As in the previous scenario, the new product can be sold at Rs. 50 per unit. Costs are as follows: Fixed Costs are Rs. 8640 for the period, Variable Costs are Rs. 30 per unit, and the Production Capacity is 900 units per period.

14. BUSINESS MATHEMATICS & STATISTICS