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TANAPMATH$76\mathrm{.}2\mathrm{.}023.$

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Formulate but do not solve the following exercise as a linear programming problem.

Custom Office Furniture Company is introducing a new line of executive desks made from a specially selected grade of walnut. Initially, three different models$$A$,$ B$,$ and C$$are to be marketed. Each model A desk requires

$1$

$1$

$4$

hr for fabrication, $1$ hr for assembly, and $1$ hr for finishing; each model B desk requires

$1$

$1$

$2$

hr for fabrication, $1$ hr for assembly and $1$ hr for finishing; each model C desk requires

$1$

$1$

$2$

hr$,$

$3$

$4$

hr$,$

$1$

$2$

hr for fabrication, assembly, and finishing, respectively. The profit on each model A desk is $$27,$ the profit on each model B desk is $$30,$ and the profit on each model C desk is $$21.$ The total time available in the fabrication department, the assembly department, and the finishing department in the first month of production is $295$ hr$,215$ hr$,$ and $185$ hr$,$ respectively. To maximize Custom's profit, P $($in dollars$),$ how many desks of each model $($x model A desks, y model B desks and z model C desks$)$ should be made in the month?

Maximize P $=$

Correct: Your answer is correct.

subject to the constraints

fabrication

Incorrect: Your answer is incorrect.

assembly

finishing

x $>=0$

y $>=0$

z $>=0$