SCM 352 Assessment 1 Student ID ______
1 (30 pts) Wild Dog Food Company wishes to introduce a new brand of dog biscuits composed of steak and duck flavored biscuits. The biscuits must contain one of each kind of two nutrients, nutrient C and nutrient D. The steak flavored biscuit contains two units of nutrients C and three units of nutrient D. The duck flavored biscuit contains one unit of nutrient C and two units of nutrient D. The FDA requires that there be at least 40 units of nutrient C and 50 units of nutrient D in a box of biscuits. The company has decided that there will be no more than 20 duck flavored biscuits in a box. It cost five cents to make a duck flavored biscuit and it cost three cents to make a steak flavored biscuit. What is the optimal product mix for a box of biscuits in order to minimize the Wild Dog's cost? Formulate the LP model..
Decision Variable:
Objective Function:
Constraints:
2. (20 pt.) The KJ company has three new position in management open -- design director, packaging director, and promotion director. There are three candidates being considered for each position. The table below gives each candidates rating for the position. Give the LP model l that would decide which applicant was give which position.
Applicant / Design / Packaging / Promotion
1 / 3 / 5 / 4
2 / 4 / 4 / 4
3 / 3 / 5 / 4
Decision Variable:
Objective Function:
Constraints:
3.(20 pts) WMW has two factories and two warehouses. The table below gives the cost of shipping from each factory to each warehouse, the capacity of each factory and of each warehouse. Restate the verbal model as a LP model
Factory / Warehouse 1 / Warehouse 2 / Capacity
Factory 1 / $3 / $3 / 25
Factory 2 / $3 / $2 / 40
Supply House demand / 30 / 20
Decision Variable:
Objective Function:
Constraints
4. (15 pts) The Perfect Manufacturing company has discontinued the production of a certain unprofitable product line. This act created considerable excess production capacity. Management is considering devoting this excess capacity to one or more of three products; call them Product 1, Product 2, and Product 3. The available capacity on the machines that might limit output is summarized in the following table.
(Machine Hours per Week)
Milling machine / 500
Lathe / 350
Grinder / 150
The number of machine hours required for each unit of the perspective product is.
Productivity coefficient (in machine hours per unit)
Machine Type / Product 1 / Product 2 / Product 3Milling machine / 9 / 3 / 5
Lathe / 5 / 4 / 0
Grinder / 3 / 0 / 2
The sales department indicates that the sales potential for Product 1 and Product 2 exceeds the maximum production rate and that sales potential for Product 3 is no more than 20 units. The profit is $50, $20, and $25 respectively on products 1, 2, and 3. The object is to determine how much of each product should be produced to maximize profit Formulate the LP model.
Decision Variable:
Objective Function:
Constraints