Problem 1: Hoke’s Spokes

John Hoke owns Hoke’s Spokes, a bicycle shop. Most of John’s bicycle sales are customer orders; however, he also stocks bicycles for walk-in-customers. He stocks three types of bicycles: (1) road-racing, (2) cross-country, and (3) mountain. A road-racing bike costs $1,200, a cross-country bike costs $1,700, and a mountain bike costs $900. He sells road-racing bikes for $1,800, cross-country bikes for $2,100, and mountain bikes for $1,200. He has $12,000 available this month to purchase bikes. Each bike must be assembled; a road-racing bike requires 8 hours to assemble, a cross-country bike requires 12 hours, and a mountain bike requires 16 hours. He estimates that he and his employees have 120 hours available to assemble bikes. He has enough space in his store to order 20 bikes this month. Based on past sales, John wants to stock at least twice as many mountain bikes as the other two combined because mountain bikes sell better.

You have been hired by John Hoke to assist in this decision-making task!
a. Formulate this problem.
b. Generate the solution.
c. Which constraints are binding? Non-binding?

Problem 2: Sklenka Ski Company

Sklenka Ski Company (SSC) is a small manufacturer of two types of popular all-terrain snow skis, the Jordanelle and the Deercrest models. The manufacturing process consists of two principal departments: fabrication and finishing. The fabrication department has 12 skilled workers, each of whom works 7 hours per day. The finishing department has 3 workers, who also work a 7-hour shift. Each pair of Jordanelle skis requires 3.5 labor-hours in the fabricating department and 1 labor-hour in finishing. The Deercrest model requires 4 labor-hours in fabricating and 1.5 labor-hours in finishing. The company operates 5 days a week. SSC makes a net profit of $50 on the Jordanelle model and $65 on the Deercrest model. In anticipation of the next ski-sale season, SSC must plan its production of these two models. Because of the popularity of its products and limited production capacity, its products are in high demand, and SSC can sell all it can produce each season. The company projects the number of Deercrest skis sold to be at least twice the number of Jordanelle skis sold. The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.

You have been hired by SSC to assist in this decision-making task!
a. Formulate this problem.
b. Generate the solution.
c. Which constraints are binding? Non-binding?

Problem 1: Hoke’s Spokes John Hoke owns Hoke’s Spokes, a bicycle...