Answer: The manufacturer should produce; Model A = 80 units, and Model B = 32 units.
Step-by-step explanation: The available time for assembly and packaging of both models have been provided as follows;
Total assembly time = 3200 minutes
Total packaging time = 960 minutes
From the information given, model A requires 32 minutes to assemble and model B requires 20 minutes to assemble. We can express this as an equation as follows;
32A + 20B = 3200 ———(1)
Also model A requires 8 minutes to package and model B required 10 minutes to package. This too can be expressed as follows;
8A + 10B = 960 ———(2)
We now have a pair of simultaneous equations which we shall solve using the elimination method. Multiply equation equation (1) by 10 and multiply equation (2) by 20 and we now have;
320A + 200B = 32000 ———(3)
160A + 200B = 19200 ———(4)
Subtract equation (4) from equation (3)
160A = 12800
Divide both sides of the equation by 160
A = 80
We can now substitute for the value of A into equation (1)
32(80) + 20B = 3200
2560 + 20B = 3200
Subtract 2560 from both sides of the equation
20B = 640
Divide both sides of the equation by 20
B = 32
Therefore in order to maximize profit for the given week, the manufacturer should produce 80 units of model A and 32 units of model B. This would yield a total value of;
(Model A) 80 x 10 = $800
(Model B) 32 x 8 = $256
Total sales for the week = 800 + 256
Total sales for the week = $1,056