Question

Burger Office Equipment produces two types of desks, standard and deluxe. Deluxe desks have oak tops and more­expensive hardware and require addi­ tional time for finishing and polishing. Standard desks require 70 board feet of pine and 10 hours of labor, whereas deluxe desks require 60 board feet of pine, 18 square feet of oak, and 15 hours of labor. For the next week, the company has 5,000 board feet of pine, 750 square feet of oak, and 400 hours of labor available. Standard desks net a profit of $225, and deluxe desks net a profit of $320. All desks can be sold to national chains such as Staples or Office Depot.

What is the correct constraint for pine wood availability in Problem 13.3?

	A)	130*Pine < 5000
	B)	70*Standard + 60*Deluxe <= 5000*Pine
	C)	70*Standard + 60*Deluxe <= 5000
	D)	Pine <= 5000

Answer 1

Soln : Let' s say that no. of standard desks = X and no. of Deluxe desk = Y

In that case as given by given parameters, we can say that 18*Y <= 750 or Y <= 41.67, Y<41

Also, We can say that 15*Y <= 400 , Y< = 26.67, or Y < 26

10*X <= 400 or X <= 40

10*X +15*Y = 400 or 2X + 3Y = 80

And, 70* X + 60* Y <= 5000

Here, Option B is wrong as right hand side cannot be 5000*Pine

Option D is also incorrect as Pine = 5000 and not <

Option C is also wrong as we can see that Y < 26 and when we consider Y = 25 , we can evaluate the value of X = 50, when putting it in eqn C.

So, 70* standard + 60* deluxe can not be equal to 5000 in any case

Option A is correct as 70 Pines(X) + 60 Pines(Y) <5000. As this will always be true.