Answer:
The answer to both a and b is in the explanation below
Explanation:
a) The increase in wage can either decrease or increase the hours worked. This is became an increase in wage has both substitution effect and income effect that work in different directions. Substitution effect An increase in wage increases the opportunity cost of leisure, thereby making the worker increase number of hours worked. Income effect The increase in wage also makers the worker richer, thereby making the worker decrease number of hours worked.
Since no information about worker's preferences is given, we do not Imow which effect will dominate the other effect and, therefore, we do not know what the net impact of the increase in wage will be.
b) The bonus will only have income effect. The bonus will make the workers richer, thereby making the worker decrease number of hours worked.
If in part a), the substitution effect and income effect are equal in magnitude, then there will be no change in the number of hours worked. The number of hours worked will remain the same at 2000 hours. Since the employer would be paying $5 extra on each hour worked, the cost to the employer of increase in wage would be $10,000 (=2000 x $5), which is the same as the bonus in part b).
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The chip manufacturer can maximize the monthly profit by using the objective function: z = 6X₁ + 7X₂ + 10 X₃
An objective function is a function that has the goal of maximizing or minimizing the model's value based on the relationship between the variables in the function.
The term "decision variables" refers to a group of variables that are responsible for regulating the objective function.
The decision variable for the quantity of the product 1, 2, 3 manufactured can be expressed as:
The objective function used in maximizing the profit is:
This is subjected to the constraint:
- 2X₁ + 3X₃ ≤ 120 (Tech A time and manufacturing limitation)
- 2.5X₁ + 3X₂ ≤ 120 (Tech B time and manufacturing limitation)
- 4X₂ ≤ 120 (Tech C time and manufacturing limitation)
- 3.5X₂ ≤ 120 (Tech D time and manufacturing limitation)
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