Question

A married couple can choose how long each partner would like to work. Partner A is paid $19 per hour and partner B is paid $31 per hour. For taxation reasons they agree neither partner should earn more than $750 more than the other per week and that the total number of hours they work should not exceed 80 hours per week.
(a) How many hours should each work per week in order to meet these constraints and achieve the maximum income? Show all your working for problem formulation and pathway to the solution. Also state the solution in plain English so it makes sense when provided to the couple.
(b) Suppose it is decide that, in addition, neither partner should work more than 9 hours more than the other. What is the solution now? What does this mean for the couple’s total workload and income?

Answer 1

Old question but I will attempt to answer.

let a = number of hours worked by partner A and b = hours worked by partner B

the money earned by A = 19a and money earned by B is 31b

|a - b| must be less than or equal to 750 and a + b must be less than or equal to 80

Answer 2

My suggestion would be to graph these constraints and find the maximum value