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.
If there are x and y of A and B, then the constraints are
3x+4y <= 1000
6a+3b <= 22*60
The profit function is
p(x,y) = 2.00x + 1.50y
When you figure out the question you want to answer, this should help.
To determine the number of hibachis that Kane Manufacturing can produce for each model, we need to compare the available resources (cast iron and labor) with the requirements to produce each model.
Let's calculate the maximum number of model-A hibachis that can be produced first:
Available cast iron: 1000 lb
Cast iron requirement for each model-A hibachi: 3 lb
Maximum number of model-A hibachis = Available cast iron / Cast iron requirement for each model-A hibachi
Maximum number of model-A hibachis = 1000 lb / 3 lb ≈ 333.33
However, since we cannot have a fraction of a hibachi, the maximum number of model-A hibachis that can be produced per day is 333 hibachis.
Now, let's calculate the maximum number of model-B hibachis that can be produced:
Available cast iron: 1000 lb
Cast iron requirement for each model-B hibachi: 4 lb
Maximum number of model-B hibachis = Available cast iron / Cast iron requirement for each model-B hibachi
Maximum number of model-B hibachis = 1000 lb / 4 lb = 250
Since we cannot have a fraction of a hibachi, the maximum number of model-B hibachis that can be produced per day is 250 hibachis.
Next, let's calculate the maximum number of hibachis that can be produced based on labor availability:
Available labor-hours: 22 hours
Labor requirement for each model-A hibachi: 6 min = 6/60 = 0.1 hours
Labor requirement for each model-B hibachi: 3 min = 3/60 = 0.05 hours
Maximum number of model-A hibachis based on labor = Available labor-hours / Labor requirement for each model-A hibachi
Maximum number of model-A hibachis based on labor = 22 hours / 0.1 hours = 220
Maximum number of model-B hibachis based on labor = Available labor-hours / Labor requirement for each model-B hibachi
Maximum number of model-B hibachis based on labor = 22 hours / 0.05 hours = 440
Now, let's compare the maximum possible production for each model based on both cast iron and labor:
Maximum number of model-A hibachis = 333 (based on cast iron)
Maximum number of model-A hibachis = 220 (based on labor)
Maximum number of model-B hibachis = 250 (based on cast iron)
Maximum number of model-B hibachis = 440 (based on labor)
To determine the actual number of hibachis that can be produced for each model, we need to consider the smaller value from the two calculations for each model.
Actual number of model-A hibachis = Smaller value between 333 and 220 = 220 hibachis
Actual number of model-B hibachis = Smaller value between 250 and 440 = 250 hibachis
Finally, let's calculate the profit for each model:
Profit for each model-A hibachi = $2
Profit for each model-B hibachi = $1.50
Total profit for model-A hibachis = Actual number of model-A hibachis × Profit for each model-A hibachi
Total profit for model-A hibachis = 220 hibachis × $2 = $440
Total profit for model-B hibachis = Actual number of model-B hibachis × Profit for each model-B hibachi
Total profit for model-B hibachis = 250 hibachis × $1.50 = $375
Therefore, Kane Manufacturing can produce 220 model-A hibachis and 250 model-B hibachis per day, resulting in a total profit of $440 for model-A hibachis and $375 for model-B hibachis.