Question

Two models of a product Regular (X) and Deluxe (Y) are produced by a company. A linear programming model is used to determine the production schedule. The formulation is as follows:

Maximize profit

$50X+60Y$

Subject to:	$8X+10Y\le 800$ (labor hours)
	$X+Y\le 120$ (total units demanded)
	$4X+5Y\le 500$ (raw materials)
	all variables $\ge 0$

The optimal solution is $X=100Y=0.$
How many units of the labor hours must be used to produce this number of units?

• A. $400$
• B. $200$
• C. $500$
• D. $20$
• E. None of the above

Answer 1

The correct option is E None of the above

Given: Maximum: $50X+60Y$

Subject to: $8X+10Y\le 800$

$X+Y\le 120$

$4X+5Y\le 500$

(i) $8x+10y\le 800$

$x$	$0$	$100$
$y$	$80$	$0$

(ii) $x+y\le 120$

$x$	$0$	$120$
$y$	$120$	$0$

(iii) $4x+5y\le 500$

$x$	$0$	$125$
$y$	$100$	$0$

Corner points Value of $z(50x+60y)$

$B(0,80)$ $4800$

$O(0,0)$ $0$

$A(100,0)$ $5000$

The optional solution Rs $5000$ at $x=100y=0$

The units of labor hours is $5000$.