MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
A furniture manufacturer makes chairs and tables. Each chair requires 2 hours of woodworking and 1 hour of finishing, while each table requires 3 hours of woodworking and 2 hours of finishing. The workshop is available for at most 60 hours of woodworking and 40 hours of finishing per day. The manufacturer must produce at least 10 chairs daily. Let x and y denote the number of chairs and tables produced per day respectively.
(i) Formulate all the constraints on x and y as linear inequalities.
(ii) For the production plan P(12,8), determine whether the plan is feasible. Justify your answer with calculations.
(iii) For the production plan Q(15,10), determine whether the plan is feasible. If it is not, state the specific constraint(s) that are violated, and calculate the minimum number of tables that must be reduced (keeping the number of chairs fixed) so that the adjusted plan becomes feasible.