Jenna works as a babysitter on weekend nights, for a maximum of 10 hours per wee

Question

Jenna works as a babysitter on weekend nights, for a maximum of 10 hours per weekend. She usually babysits for the Smiths, who pay her 5 dollar an hour, and the Garcias, who pay her 6 dollars an hour. The Smiths have very young children so they need Jenna at least 4 hours every weekend; on the other hand, the Garcias usually ask Jenna to babysit for a maximum of 3 hours per weekend.Jenna wants to earn the most money from her babysitting hours. What is the equation that represents Jenna's babysitting money earned in one weekend? Which are the restrictions for the variables? What is the geometric shape of the feasible set? How many hours should Jenna babysit for each of the families each weekend to earn the most money? What are Jenna's maximum earnings per weekend?

Explanation / Answer

Let the number of hours worked at Smiths be x

Let the number of hours worked at Garcias be y

a) Equation for babysitting money

z = 5x + 6y

b) Constraints

x>=4

y<=3

c) The geometric shape of the feasible set is linear, since the profit function is linear function of x and y

d) Jenna should work 3 hours (maximum) for Garcias and remaining (10-3) = 7 hours for Smiths

e) Jenna maximum earnings

z = 5(7) + 6(3) = 35 + 18 = 53$

Hence the maximum earnings for Jenna is equal to 53$

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