Please see the following attached Word document. These two multiple choice questions involve determining the objective function that will maximize the profit of CQE Inc, as well as determining the con

Please see the following attached Word document. These two multiple choice questions involve determining the objective function that will maximize the profit of CQE Inc, as well as determining the constraint for packaging. Any help would be much appreciated. Please show all your work with how you arrived at the answers.

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Use the following information to answer Question 20 and 21.
In order to increase its profit, CQE Inc. is considering the possibility of adding a new
product, a calculator, to its product line. Three different types of calculator can be
manufactured, each requiring a $ 100,000 investment. The information concerning each
calculator is shown below:
Model
Sales
(Units)
Price
Cost of
Materials
Labour
Hours
Overhead
Costs
1
50,000
$55
$15
1.0
$9
2
300,000
$27
$12
0.2
$10
3
100,000
$35
$13
0.5
$7
The labour cost is $16 per hour, and 60% of overhead costs are variable. There are
3,000 hours available each month for the production of these calculators. In order to
ship the calculators, the company has 27,000 boxes available. CQE can pack four
calculators of type 2 or four calculators of type 3 in one box, whereas only one type 1
calculator fits in a box. Where:
X1 = quantity of calculator 1
X2 = quantity of calculator 2
X3 = quantity of calculator 3
20) What is the objective function that will maximize the profit (Max Z) of the company?
a) Max Z = 55X1 + 27X2 + 35X3
b) Max Z = 20.4X1 + 7.8X2 + 11.2X3
c) Max Z = 18.6X1 + 5.8X2 + 9.8X3
d) Max Z = 15X1 + 1.8X2 + 7X3 – (100,000 × 3)
e) None of the above
21) What is the constraint for packaging?
a) X1 +(.25) X2 + (.25)X3 <= 27,000 b) X1 + X2 + X3 <= 27,000 c) X1 + 4X2 + 4X3 <= 27,000 d) 0.25X1 + X2 + X3 <= 27,000 e) None of the above

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