Agricultural Studies 3300, Fall 2004
Agricultural Systems Modeling
Assignment # 3
Due: Friday October 8th
Lab Instructor: Jeff Davidson
1.
A firm uses 2 machines in the manufacture of 2 products. Product A. requires 3 hours on
machine 1 and 5 hours on machine 2. Product B requires 6 hours on machine 1 and 4
hours on machine 2. If 36 hours of machine 1 time and 42 hours of machine 2 time are to
be scheduled, determine the product mix that fully utilizes the machine time.
2.
A firm is interested in determining the breakeven production for a new product. The cost
of introducing the product is estimated to be $80,000. This cost includes initial
advertising and promotion as well as the fixed cost necesary for one year of production.
The variable cost per unit is $35, and the proposed selling cost is $60.
A) Determine breakeven production.
B) Determine the profit on sales of 2000 units
3.
Establish linear functions for the following problems
a.)
b.)
Costs are $6000 when output is 0 and $8000 when output is 1500 units
If 1000 units can be sold at a price of $5.00 per unit and 2000 units can be sold at
a price of $4.00 per unit, determine price as a function of the number of units sold.
4.
Develop an inequality for the following problem and give the domain of the variables
A calf needs a minimum of 300 units of a special dietary supplement each day. This
supplement is available in two commercial products, A and B. Each ounce of A contains
25 units of the supplement and each ounce of B contains 40 units.
5.
The profit function for the new fletchers plant is described by a quadratic function. The
following data points were estimated by the chief accountant. Zero pigs results in a loss
of $10 million. 6000 pigs per day results in a profit of $8 million and 8000 pigs per day
results in a profit of $6 million. Determine the quadratic function that describes profit as
a function of the number of pigs per day.
6.
A farmer has plenty of bags of fertilizers of three types. These three types contain potash, nitrate and
phosphate with 2:1:0, 1:1:1, and 0:2:1 units respectively in each bag of the three types. For the best yield,
an acre of land requires 12 units of potash, 8 units of nitrate and 4 units of phosphate. Determine the right
numbers of bags of each type required for the best yield.
7.
A class A chemical spraying license requires 6 hours of type 1 training and 10 hours of
type 2 training. A class B spraying license requires 12 hours of type 1 training and 8
hours of type 2 training. If 72 hours of type 1training time and 84 hours of type 2 training
time are to be scheduled, determine the number of trainees that fully utilizes the training
time.