Kane Manufacturing has a division that produces two models of hibachis, model A and model B. To produce each model-A hibachi requires 3 lb of cast iron and 6 min of labor. To produce each model-B hibachi requires 4 lb of cast iron and 3 min of labor. The profit for each model-A hibachi is $2, and the profit for each model-B hibachi is $1.50. There are 1000 lb of cast iron and 22 labor-hours available for the production of hibachis each day.

Question

How many hibachis of each model should the division produce to maximize Kane's profit?
model A
______hibachis
model B
______hibachis

What is the largest profit the company can realize?
$_____

Answer 1

Do this graphically:
Let the y axis be Model A, x axis Model B.
Now consider cast iron. On the Y axis, mark the point 0,333 (the point of all model A and all the iron). then on the x axis, mark 250,0 (all cast iron used on B). connect the points, that is the IRON constraint line.
Now consider manhours. On the Y axis, plot (0,220) the point if all labor hours were making ModelA. Then plot the point (440,0), connect the points, that is the labour hour constraint.

Now all the points within x,y axis, and below any of the lines is the area of possible solutions. There is a nice theorem that tells us the max and min will be somewhere on the boundries at a endpoint. So examine for profit at 0,220, and 250,0, and the crossing point of the iron/labour lines. Compute profit at each of those points
Profit=x*1.50+y*2

I didn't make a accurate graph, just a mental sketch, but in my head it looks like the vicinity of x= about 150 (model b) and y= about 90. Work that out accurately.