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Sample Quantitative Questions Chapter 3

Sample Quantitative Questions Chapter 3. Ted Mitchell. 1) Calculate the meta-conversion rate from two observations. You have observed two coffee shop performances Observation #1: open 100 hours and sold 10,000 cups of coffee at a rate of 100 cups per hour, cph

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Sample Quantitative Questions Chapter 3

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  1. Sample Quantitative QuestionsChapter 3 Ted Mitchell

  2. 1) Calculate the meta-conversion ratefrom two observations • You have observed two coffee shop performances • Observation #1: open 100 hours and sold 10,000 cups of coffee at a rate of 100 cups per hour, cph • Observation #2 open 120 hours and sold 10,800 cups of coffee at a rate of 80 cups per hour, cph • What is the meta-conversion rate, m?

  3. 1) Calculate the meta-conversion ratefrom two observations • Meta-coffee hours marketing machine is • Difference in output = (meta-conversion rate, m)x difference in input • ∆Q = (meta-conversion rate, m) x ∆hours • Measure Difference in output, ∆Q = Q2-Q1 ∆Q = 10,800 – 10,000 = 800 cups • Measure Difference in Input, ∆H = H2-H1∆H = 120 hours -100 hours = 20 hours • Calculate Meta-conversion rate, m = ∆O/∆H • Meta-conversion rate, m = 800 cups/20 hrs = 40cph

  4. 1) Calculate the meta-conversion ratefrom two observations

  5. #2 Forecast a change in output, ∆O, from a Meta-Marketing Machine • You know the calibrate meta-machine that explains the differences in observed performances for coffee sales, ∆Q, from store hours, ∆H is represented as • Output, ∆Q = 40cph x Input, ∆H • The boss is proposing a decrease in the number of store of ∆H = -5 hours • What is the forecasted change in the number of number of cups sold, ∆Q? • ∆Q = 40cph x -5 hours = -200 cups

  6. 2) Forecast a Change in output, ∆O, from a Meta-Marketing Machine

  7. #3 Forecast an Actual Output • In week 2 you are open for 120 hours a week and are selling 10,800 cups of coffee at at rate of 80 cups per hours. • The Boss is proposing a reduction in store hours of 5 hours a week and you have forecasted a 200 cup reduction in sales in week 3. • Three related questions • 1) What is the proposed number of hours in week 3? • H3 = 120 hours – 5 hours = 115 hours • 2) What is the forecasted sales volume in week 3? • Q3 = 10,800 cups - 200 cups = 10,600 cups • 3) What is the forecasted rate of sales per hour • Conversion rate, r = Q/H = 10,600/115 = 92.17 cph

  8. #3 Forecast a Specific Output and Conversion Rate The forecasted conversion rate, r, is notthe meta-conversion rate, m

  9. Forecasting a specific outcome is awkward when using the single point slope equation of the meta-marketing ‘coffee sales from hours’ machine • Change in Coffee sales = meta-conversion rate, m) x Change in store hours

  10. 5) Construct a slope-intercept equation of a meta-marketing machine • Market research has provided you with a calibrated equation of the single point slope equation of a meta-marketing machine • Change in Coffee sales, ∆Q = (meta-conversion rate, 40 cph) x Change in store hours, ∆H ∆Q = 40 cph x ∆H • (Q3-10,800 cups) = 40cph x (H3 – 120 hours) • What is the y-intercept of the slope-intercept equation of the meta-marketing machine? • Set H3 = zero and Q3 = value of y-intercept, a • a -10,800 cups = 40 cph x (0-120 hours) • a = 10,800 cups - 4,800 cups • a = 6,000 cups sold when the store is closed??? • What is the slope-intercept equation of the meta-marketing machine? • Forecasted Cups sold, Q = 6,000 cups + (40 cps)(Hours open, H)

  11. Q = kHh Quantity, Q Q = 6,000 + 40cps(H) Q = kHh x x x x x x x x x x x x x x x x x x x x Linear Meta-Machine is a secant that approximates the Quantity sold as a function of hours open H= Hours Open

  12. 6) Forecast an output from the slope-intercept equation given a proposed level of input • Market research department has provided an estimate of the relationship between hours the store is open and the number of cups that is sold as a slope-intercept equation • Q = a + m(H) • Forecasted Cups sold, Q = 6,000 cups + (40 cph)(Hours open, H) • It is proposed to stay open for 105 hours a week. What is the forecasted sales volume for staying open that many hours? • Cups sold, Q = 6,000 cups + (40 cph)(105 hours) • Cups sold, Q = 6,000 cups + 4,200 cups = 10,200 cups

  13. 7) Forecast a quantity sold from a proposed price tag • Market Research has provided you with the slope-intercept equation which they are calling a demand curve given the price tag on each cup, P, is an input • Q = a – m(P) • Quantity Demanded, Q = 6,000 cups -900 cpP x Price tag, P • When the price is $4.00 for a cup what is the forecasted quantity of cups sold, Q? • Quantity, Q = 6000 cups – 900 cp$ x ($4) • Quantity, Q = 6000 cups – 3,600 cups = 2,400 cups

  14. LowerPrice Sells More Units Quantity Sold Demand Equation Q = 6,000 – 900(P) 2,400 Revenue = 2,400 x $4.00Revenue = $9,600 Price per Cup $3.90 $4.00 TJM

  15. The Demand Equation • Q = a – m(P) • Often called price equation is • The Slope-Intercept equation of the meta-marketing machine that produces a quantity sold, Q, using the price tag, P, as an input

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