Question

A company produces two products, A and B, and has a production capacity of 500 units per day. Product A requires 2 hours of labor and 1 hour of machine time to produce, while product B requires 1 hour of labor and 2 hours of machine time. The company has 1000 hours of labor and 1000 hours of machine time available. Product A sells for $20 per unit, and product B sells for $10 per unit. How many units of each product should the company produce to maximize revenue? Solve using graphics technique.

Answer 1

2x + y \(\le\) 1000

x + 2y \(\le\) 1000

x, y >, 0

Max. Z = 20x + 10y

To draw 2x + y = 1000

x	500	0	\(\frac{1000}{3}\)
y	0	1000	\(\frac{1000}{3}\)

To draw x+ 2y = 1000

x	1000	0	\(\frac{1000}{3}\)
y	0	500	\(\frac{1000}{3}\)

Corner points	z = 20x + 10y
0(0,0)	0
A(500,0)	10000
D(0,500)	500
c(\(\frac{1000}{3},\frac{1000}{3}\))	10000

Max.Revenue is $3000.