Answer:
(140, 160)
Step-by-step explanation:
Let x represent model A and y represent model B.
2 lb of cast iron is needed for model A while 4 lb of cast iron is needed for model B. 920 lb of cast iron is available for production. This can be represented by the constraint:
2x + 4y ≤ 920 (1)
7 min of labor is needed for model A while 4 min of labor is needed for model B. 1620 min of labor is available for production per day. This can be represented by the constraint:
7x + 4y ≤ 1620 (2)
Also, x ≥ 0
, y ≥ 0
Plotting the constraints using geogebra app, The points that satisfy these constraints are:
(0, 230), (231.42, 0), (0,0) and (140, 160)
The profit for each model A grate is $1.50, and the profit for each model B grate is $2.40. The profit equation is:
Profit = 1.5x + 2.4y
We are to maximize profit. Hence:
At (0,0); max Profit = 1.5(0) + 2.4(0) = 0
At (0,230); max Profit = 1.5(0) + 2.4(230) = 552
At (231.42,0); max Profit = 1.5(231.42) + 2.4(0) = 347
At (140,160); max Profit = 1.5(140) + 2.4(160) = 594
The maximum profit is at (140, 160)