Answer:
The company will produce the requested 150 units of A for a gain of 300 dollars
and then use his resourses to produce B yielding a gain of 90 dollars
total of 390 profit
Explanation:
The company will produce at least 150 units of product A therefore:
lbs used: 150 x 3 = 450
minutes of labor used 150 x 8 = 1,200
leaving available:
1,200 - 450 = 750 lbs
1,500 - 1,200 = 300 mins
As time is the most scarce resource we allocate base on thecontribution per minute:
product A $2 of profit for 8 minutes: 0.25 dollars per minute
product B $1.5 of profit for 5 minutes: 0.30 dollars per minute
As product B is more profitable considering labor time we use the entire amount left to produce product B
300 min / 5 minutes = 60 units of b
Kane should produce 60 of model A and 204 of model B to maximize profit
Represent model A with x and model B with y.
So, we have the following parameters
x y Available
Pounds 3 5 1200
Labor 8 5 1500
Profit $2.00 $1.50
From the above table, we have the objective function to be:
Max P = 2x + 1.5y
Subject to
3x + 5y ≤ 1200
8x + 5y ≤ 1500
x, y ≥ 0
By plotting the constraints (see attachment), we have the following feasible points
(x,y) = (0,300) (60,204) and (400,0)
Substitute these values in the objective function
P(0,300) = 2*0 + 1.5 * 300 = 450
P(60,204) = 2*300 + 1.5 * 204 = 906
P(400,0) = 2*400 + 1.5 * 0 = 800
The maximum profit is at (60,204)
Hence, Kane should produce 60 of model A and 204 of model B to maximize profit
Read more about objective functions at:
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