Question 1

A positive value for the labour input slack variable implies:&#10;A)no excess capacity.&#10;B)use of more labour resources than are available.&#10;C)use of less labour resources than are available.&#10;D)expansion is warranted provided the slack variable value is less than the market wage rate.

Accepted Answer

A

Question 2

When output is maximized subject to a labour constraint, the shadow price of labour is the:&#10;A)marginal product of labour.&#10;B)marginal revenue product of labour.&#10;C)market price of labour.&#10;D)amount paid for labour.

Accepted Answer

The shadow price of labour, when output is maximized subject to a labour constraint, is the marginal product of labour, which represents the additional output produced by an additional unit of labour.

Question 3

If QA > 0, then the marginal value of output:&#10;A)equals the marginal value of inputs employed.&#10;B)is less than the marginal value of inputs employed.&#10;C)exceeds the marginal value of inputs employed.&#10;D)none of these.

Accepted Answer

When QA > 0, it implies that the firm is producing output. In a competitive market, the marginal value of output (price) equals the marginal cost of production, which includes the marginal value of inputs employed. Hence, the marginal value of output equals the marginal value of inputs employed.

Question 4

When an LP objective function is to minimize cost:&#10;A)constraint conditions must be of the variety.&#10;B)constraint conditions must be of the variety.&#10;C)all costs must be variable.&#10;D)the total cost function must not be linear.

Accepted Answer

The answer of When an LP objective function is to...

Question 5

When the objective function coincides with a single point in the feasible space:&#10;A)an optimal solution cannot be determined.&#10;B)there is only one optimal solution.&#10;C)there are many possible optimal solutions.&#10;D)an optimal solution does not exist.

Accepted Answer

If the objective function coincides with a single point in the feasible space, it means that there exists only one feasible solution that satisfies all the constraints and also optimizes the objective function. Hence, there is only one optimal solution. If the objective function coincides with a single point in the feasible space, then there is only one point in the feasible space that satisfies the constraints and also optimizes the objective function. Therefore, there is only one optimal solution.

Question 6

The profit function = aQX + bQY, can be written as QY = /b - a/bQY where a and b are the profit contributions of products X and Y, respectively.If both profit contributions increase by a fixed percentage, isoprofit line:

A)slope decreases.
B)slope is unaffected.
C)slope increases.
D)none of these.

Accepted Answer

The isoprofit line is determined by the profit function, so as long as the ratio between a and b remains the same, the slope of the isoprofit line will not be affected by a fixed percentage increase in both profit contributions. Therefore, the correct answer is B. The slope of the isoprofit line is determined by the ratio of the profit contributions of products X and Y, i.e. a/b. If both profit contributions increase by the same percentage, the ratio of a/b remains the same and therefore the slope of the isoprofit line is unaffected.

Question 7

If X = 0 in the primal solution:&#10;A)the marginal value of inputs just equals the marginal value of output in X production.&#10;B)the marginal value of inputs exceeds the marginal value of output in X production.&#10;C)LX = 0 in the dual solution.&#10;D)LX < 0 in the dual solution.

Accepted Answer

When X = 0 in the primal solution, it indicates that producing X is not optimal given the current constraints and prices. This happens when the marginal value of inputs (the cost to produce one more unit of X) exceeds the marginal value of output (the revenue or benefit from producing one more unit of X), making production unprofitable or less profitable compared to other uses of the resources.

Question 8

When the primal LP problem is to minimize cost subject to various output constraints, the shadow prices in the dual constraints:&#10;A)equal the marginal revenue product of each input.&#10;B)are positive for inputs with excess capacity.&#10;C)equals zero for fully utilized inputs.&#10;D)none of these.

Accepted Answer

The answer of When the primal LP problem is to...

Question 9

If the labour slack variable > 0, then:&#10;A)excess labour capacity exists.&#10;B)the shadow price on labour is > 0.&#10;C)the shadow price on labour is < 0.&#10;D)the marginal revenue product of labour > 0.

Accepted Answer

Labour slack refers to the gap between the actual and required amount of labour. If the labour slack variable is > 0, it means that there is excess labour capacity available in the market. This implies that there are more workers seeking jobs than there are employment opportunities. Hence, the best choice is A - excess labour capacity exists. Labour slack refers to the difference between the actual number of employees and the optimum number of employees required for efficient production. If the labour slack variable is greater than zero, it means that the actual number of employees is less than the optimal number, which indicates that there is excess labour capacity or underutilization of labour resources.

Question 10

If the primal objective function is to maximize profit subject to input constraints, the dual objective function is to minimize:&#10;A)total cost.&#10;B)explicit costs.&#10;C)the quantity of output.&#10;D)the value of inputs employed.

Accepted Answer

The answer of If the primal objective function is to...

Deck 9: Linear Programming