David, LaDeana, and Lydia are the sole partners and workers in a company which produces fine clocks. David and LaDeana each are available to work a maximum of 40 hours per week at the company, while Lydia is available to work a maximum of 20 hours per week.
The company makes two different types of clocks: a grandfather clock and a wall clock. To make a clock, David (a mechanical engineer) assembles the inside mechanical parts of the clock while LaDeana (a woodworker) produces the handcarved wood casings. Lydia is responsible for taking orders and shipping the clocks. The amount of time required for each of these tasks is shown below

Each grandfather clock built and shipped yields a profit of $300, while each wall clock yields a profit of $200.
The three partners now want to determine how many clocks of each type should be produced per week to maximize the total profit.
(a) Formulate a linear programming model in algebraic form for this problem.

Transcribed Image Text:

Time Required Task Grandfather Clock Wall Clock Assemble clock mechanism Carve wood casing Shipping 6 hours 8 hours 3 hours 4 hours 4 hours 3 hours