1. A firm manufactures tables and desks. To produce each table requires 1 hour of labor, 10 square feet of wood, and 2 quarts of finish. To produce each desk requires 3 hours of labor, 20 square feet
of wood, and 1 quart of finish. Available is at most 45 hours of labor, at most 350 square feet of
wood, and at most 55 quarts of finish. The tables and desks yield profits of $4 and $3 respectively.
Find the number of each product to be made in order to maximize profits. Find the maximum
profit.

9514 1404 393

  25 tables, 5 desks, for a profit of $115

Step-by-step explanation:

Let x and y represent the numbers of tables and desks to build, respectively. The we want to maximize 4x+3y subject to the constraints ...

  x +3y ≤ 45 . . . . . constraint on labor

  10x +20y ≤ 350 . . . . . constraint on wood

 2x +y ≤ 55 . . . . . constraint on finish

These inequalities are graphed in the attachment. The vertex of the feasible region that maximizes profit is (x, y) = (25, 5).

The product mix that maximizes profit is ...

  25 tables

  5 desks

for a profit of 25·4 +5·3 = 115 dollars.