If we let x represent the number of units sold and P the total profit, then, with a profit of $12 per unit, assuming that 6 hours are required to produce each unit and only 60 hours of production time are available per week, the following mathematical model defines the total profit earned by selling x units: Max 10x
s. t.
5x <= 40
x >= 0

Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours of production time for each unit produced. Use y as the number of units of product 2 produced.

Required:
Show the mathematical model when both products are considered simultaneously. Express your answers in terms of x and y.

An annual marathon covers a route that has a distance of approximately 26 miles. winning times for this marathon are all over 2 hours. the following data are the minutes over 2 hours for the winning male runners over two periods of 20 years each. earlier period 14 12 15 22 13 10 19 13 9 14 20 18 16 20 23 12 18 17 6 13 recent period 7 11 7 14 8 9 11 14 8 7 9 8 7 9 9 9 9 8 10 8 (a) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the earlier period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks. for more details, view how to split a stem.) minutes beyond 2 hours earlier period 0 1 2 (b) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the recent period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks.) minutes beyond 2 hours recent period (c) compare the two distributions. how many times under 15 minutes are in each distribution