Problems:
The Frey Company manufactures and sells two products a toddler bike and a toy high chair. Linear programming should be employed to determine the best production and sales mix of bikes and chairs. The approach will allow Frey to speculate on economic changes. For example, management is often interested in knowing how variations in selling prices, resource costs, resource availabilities, and marketing strategies would affect the company's performance.
The demand for bikes and chairs is relatively constant throughout the year. The following economic data pertains to the two products:
Bike (B) Chair (C)
Selling price per unit $12 $10
Variable cost per unit 8 2____
Contribution margin per unit $4 $3
Raw materials required: Bike Chair
Wood board feet 1 2
Plastic pounds 2 1
Direct labor required, hours 2 2
Estimates of the resource quantities available in a non-vacation month during the year are
Wood board feet ............. 10,000
Plastic pounds ............... 10,000
Direct labor hours ............. 12,000
a) Formulate a linear program with objectives and constraints and clearly identify all variables and constraints.
b) Graph this program identify the feasible region and potential optimal solutions.
c) What is the optimal combination of bikes and chairs that should be produced?
d) During the summer months, the total direct labor hours are reduced from 12,000 to 10,000 hours per month because of vacations. With the reduced labor hours what is the optimal product mix for each month of the summer?
e) Based on the answer in "d", what is the shadow price of direct labor hours in the original model for a month with 12,000 labor hours. Discuss what this shadow price means.