1. BUSINESS MATHEMATICS & STATISTICS

2. LECTURE 11 Review Lecture 10 Set up and manipulate ratios. Express percent differences Allocate an amount on a prorata basis using proportions. Convert currencies Relate movement to appreciation or depreciation. Interpret and use index numbers

3. RATIO Ali, Fawad and Tanveer’s partnership interests in Creative Enterprises are in the ratio of their capital contributions of Rs. 7800, Rs. 5200 and Rs.6500 respectively What is the ratio of Ali’s to Fawad’s to Tanveer’s partnership interest?.

4. RATIO Ali Fawad Tanveer 7800 : 5200 : 6500 78 : 52 : 65 Divide each by 52 1.5 : 1 : 1.25

6. Estimating Using Ratio Ratio of sales of Product X to sales of Product Y = 4:3. Sales of product X forecast to be Rs. 180,000 Sales of products maintain the same ratio? Sales of product Y ?

7. CALCULATION X : Y = 4 : 3 180,000 : Y = 4 : 3 Cross – multiply 180,000 x 3 = 4 x Y 4 x Y = 180,000 x 3 Y = (180,000 x 3)/4 Y = 135,000

9. How much more staff? 500 bed hospital 200 nurses 150 other support staff A new 100-bed wing to be opened Assuming comparable staffing levels, how many more nurses and support staff will need to be hired?

10. Calcuation Beds : Nurses : Other staff 500 : 200 : 150 100 : X? : Y? Nurses 500 : 200 = 100 : X 500 X = 200 x 100 X = (200 x 100)/500 = 40 Other staff Y = (150 x 100)/500 = 30

12. Estimating Using Ratios Punch recipe mango juice, apple juice and orange juice ratio of 3:2:1. To make 2 litres of punch calculate quantity of ingredient is needed

13. Calcuation Mango juice : Apple juice : Orange juice 3 : 2 : 1 Total = 6 X? : Y? : Z? Total = 2 litre Mango juice X = (3/6)*2 = 1 litre Apple juice Y = (2/6)*2 = 0.67 litre Orange juice Z = (1/6)*2 = 0.33 litre

15. Estimating Using Ratios Punch recipe mango juice, apple juice and orange juice ratio of 3:2:1. If you have 1.5 litres of orange juice, how much punch can you make?

16. Matrix Functions in Microsoft Excel MDETERM Returns the matrix determinant of an array MINVERSE Returns the matrix inverse of an array MMULT Returns the matrix product of two arrays

17. MINVERSE MINVERSE(array) Array is a numeric array with an equal number of rows and columns Inverse of the matrix A1:B2. Column A Column B Row 1 d/(a*d-b*c) b/(b*c-a*d) Row2 c/(b*c-a*d) a/(a*d-b*c) Array formula 1. F2 2. Enter formula 3. Ctrl + Shift + Enter

18. MINVERSE

20. MDETERM MDETERM(array) Array is a numeric array with an equal number of rows and columns Array, A1:C3, the determinant is defined as: MDETERM(A1:C3) equals A1*(B2*C3-B3*C2) + A2*(B3*C1-B1*C3) + A3*(B1*C2- B2*C1)

22. MMULT Returns the matrix product of two arrays. The result is an array with the same number of rows as array1 and the same number of columns as array2. MMULT(array1,array2) Array1, array2 are the arrays you want to multiply Array Formula

24. Calcuation Mango juice : Apple juice : Orange juice 3 : 2 : 1 Total = 6 X? : Y? : Z=1.5 Total = ? litre Mango juice X = (3/1)*1.5 = 4.5 litre Apple juice Y = (2/1)*1.5= 3.0 litre Orange juice Z = 1.5 litre Total = 4.5 + 3.0 + 1.5 = 9 litre

26. Estimating Using Ratios Punch recipe mango juice, apple juice and orange juice ratio of 3 : 2 : 1.5 If you have 500 m. litres of orange juice, how much mango juice and apple juice is needed ?

27. Calcuation Mango juice : Apple juice : Orange juice 3 : 2 : 1.5 Total = 6.5 X? : Y? : Z=500 Total = ? Mango juice X = (3/1.5)*500 = 1000 ml Apple juice Y = (2/1.5)*500= 667 ml Orange juice Z = 500 ml Total = 1000 + 667 + 500 =2167 ml

29. BUSINESS MATHEMATICS & STATISTICS