Applied linear algebraA manufacturer produces desks and bookcases. Desks d require 5 hours of cutting time and 10 hours of assembling time. Bookcases b require 15 minutes of cutting time and one hour of assembling time. Each day, the manufacturer has available 200 hours for cutting and 500 hours for assembling. The manufacturer wants to know how many desks and bookcases should be scheduled for completion each day to utilize all available work power. Show that this problem is equivelent to solving two equatinos in the two unknowns d and b.

Answer:Step-by-step explanation:Let d= number of desks and b= number of bookcases.Since each day the number of hours available for cutting is 200, then the amount of desks produced by the cutting time of one desk plus the amount of bookcases produced by the cutting time of one bookcase must be 200. This means that5d+1/4b=200Now, since each day the number of hours available for assembling time is 500, then the amount of desks produced by the assembling time of one desk plus the amount of bookcases produced by the assembling time of one bookcase must be 500. This means that10d+b=500Then, solve this problem is equivalent to solve the following linear system[tex]5d+\frac{1}{4}b=200 \\10d+b=500[/tex] in the two unknowns d and b