ECONOMICS 2B
2018
TUTOR WEEKS: 30 July to 3 August
ACTIVITY 1
:
Assume a demand function:
Q = 5000 – 10P + 40A + PA – 0.8A
2
– 0.5P
2
(where Q= quantity ; P= price and A= advertising expenditures in hundreds)
Derive/calculate the following:
Task
Answer
1. The partial derivative of price
2. The partial derivative of advertising
3. The optimal value of P
4. The optimal value of A
5. The optimal value of Q
ACTIVITY 2
:
An athlete carefully watches her intake of calcium, proteins and calories. Her
breakfast diet consists mainly of milk and cereal, whose prices and nutrient
contents appear in the following table:
Milk (10 ml)
Cereal(10
gram)
Calcium
2
2
Protein
2
6
Calories
6
2
Price
0.10
0.15
She seeks a diet that supplies at least 50 units of calcium, 90 units of protein,
and 66 calories at minimum cost.
Question
Answer
State the primal problem and the
constraint equations
1

Illustrate the feasible region with the
aid of a diagram.
(
Milk on the vertical-axis and cereal on the
horizontal-axis)
Show the corner point solutions.
Final solution.
ACTIVITY 3
:
One of the product lines of Paveco is paving. The analysts had to determine the
optimal monthly combination of
two paving technologies namely asphalt and
concrete paving aswell as the contribution per one unit of the constraint to the
profit of Paveco. In this regard the firm is mainly confronted by capacity
constraints such as a road grader, roller and power trowel time. The maximum
number of hours of road grader time available per month is 640; of roller time,
1500 and of trowel time, 150. It takes two hours of road grader time and five

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