A manufacturer produces three types of desks custom deluxe a

A manufacturer produces three types of desks: custom, deluxe, and regular. Each custom desk c requires 12 worker hours to cut and assemble and 5 worker hours to finish. Each deluxe desk d requires 10 hours to cut and assemble, and 3 hours to finish ; each regular desk requires 6 hours to cut and assemble, and 1 hour to finish. On a daily basis, the manufacturer has available 440 worker hours for cutting and assembling, and 120 worker hours for finishing. Show that The problem of determining how many desks of each type to produce so that all workpower is used is equivalent to solving two equations in the three unknowns c, d, and r. How many solutions are three?

Solution

The required equations are 12x+10y+6z=440, 5x+3y+z=120

Since we have two equations with three unknowns, there exist infinite solutions with one variable.