Question

jack and jane are married and both work. however, due to their responsibilities at home, they have decided that they do not want to work over 65 hours per week combined. jane is paid $14 per hour at her job, and jack is paid $10 per hour at his. neither of them are paid extra for overtime, but they are allowed to determine the number of hours per week that they wish to work. if they need to make a minimum of $850 per week before taxes, what is the maximum amount of hours that jack can work per week according to these limits?

a. 10

b. 50

c. 20

d. 15

Explanation:

Step1: Define variables

Let \( J \) = Jack's hours, \( N \) = Jane's hours.

Step2: Set up constraints

Total hours: \( J + N \leq 65 \)
Total income: \( 10J + 14N \geq 850 \)

Step3: Maximize Jack’s hours

To maximize \( J \), minimize \( N \). From \( J + N \leq 65 \), \( N = 65 - J \) (max possible \( J \) for given \( N \)). Substitute into income constraint:
\( 10J + 14(65 - J) \geq 850 \)
\( 10J + 910 - 14J \geq 850 \)
\( -4J \geq -60 \)
\( J \leq 15 \)

Answer:

D. 15