Problem 1: The chief scientist at the Laboratories estimates that the cost (in millions of dollars) of developing and introducing a new type of anti nuclear drug equals
C=100-19t+0.5t^2 , For 1< t < 6
Where t is the number of years taken to develop and introduce the new drug. The discounted profit (gross of innovation cost) from a new drug of this type (in millions of dollars) is estimated to equal
R= 110-15t, For 1< t < 6
a. The managers of the Laboratories are committed to developing and introducing this new drug within six years, and it is impossible to develop and introduce it in less than one year. What project duration would minimize cost?
b. Why does R decline as t increases?
c. What is the optimal project duration?
Fill in Answer Here:
a. Minimum cost occurs at the value of t where dC/dt = 0:
But this t must be within the valid range of 1 ≤ t ≤ 6.
b. Two reasons:
c. Profit, π = Revenue - Cost = R- C = .....
dπ/dt = .......
Max π occurs when dπ/dt = 0......
Problem 2:
The Hverford Company is considering three types of plants to make a particular electronic device. Plant A is much more highly automated than plant B, which in turn is more highly automated than Plant C. For each type of plant, average variable cost is constant so long as output is less than capacity, which is the maximum output of the plant. The cost structure for each plant is as follows:
Plant A Plant B Plant C
Average Variable Cost $ $ $
Labor 1.10 2.40 3.70
Materials 0.90 1.20 1.80
Other 0.50 2.40 2.00
Total 2.50 6.00 7.50
Total fixed Costs 300,000 75,000 25,000
Annual Capacity 200,000 100,000 50,000
a) Derive the average cost of producing 100,000, 200,000, 300,000, and 400,000 devices per year with plant A. ( For outputs exceeding the capacity of a single plant, assume that more than one plant of this type is built.)
b) Derive the average cost of producing 100,000, 200,000, 300,000, and 400,000 devices per year with plant B.
c) Derive the average cost of producing 100,000, 200,000, 300,000, and 400,000 devices per year with plant C.
d) Using the results of parts a through c, plot the points on the long run average cost curve for the production of these electronic devices for outputs of 100,000, 200,000, and 400,000 devices per year.
Fill in Answers Here:
a. At Q=100,000: ACA = AFCA + AVCA =
At Q=200,000: ACA = AFCA + AVCA =
At Q=300,000: ACA = AFCA + AVCA =
At Q=400,000: ACA = AFCA + AVCA =
(Note: due to plant capacity, at Q > 200,000 we need two plants with a total fixed costs of 2 x 300,000)
b. At Q=100,000: ACB = AFCB + AVCB =
At Q=200,000: ACB = AFCB + AVCB =
At Q=300,000: ACB = AFCB + AVCB =
At Q=400,000: ACB = AFCB + AVCB =
(Note: due to plant capacity, at Q > 100,000 we need as many plants to meet the increased production)
c. At Q=100,000: ACC = AFCC + AVCC =
At Q=200,000: ACC = AFCC + AVCC =
At Q=300,000: ACC = AFCC + AVCC =
At Q=400,000: ACC = AFCC + AVCC =
(Note: due to plant capacity, at all levels of Q, we need to use as many plants as necessary)
d. Use Excel or similar software to draw column chart.