The following data are for a company that produces washers and dryers.

Question

• Dryers retail for $198 and contribute $15 to profit.
• Washers retail for $499.95 and contribute $45 for profit.
• The washer blade is limited in production capacity to 50 blades, while all other components have no limits.
• Chassis assembly requires 6 person-hours for each dryer set and 18 person-hours for each washer. The plant employs 225 workers for an 8-hour shift to perform chassis assembly operations.
• A dryer requires 1 person-hour on the assembly line, a washer requires 1.6 personhours. There are 30 people on a single 8-hour shift assigned to assembly.
• Final inspection requires 0.5 person-hour for a dryer and 2.0 person-hours for a washer. The plant employs 20 full-time inspectors and one part-time employee for 2 hours per day.

a. Write a linear programming model.
b. What is the optimum number of dryers and washers?
c. Calculate the maximum profit.
d. The linear-programming and break-even approaches are used to find the selling price for both the dryer and the washer, based on $10,000 fixed cost for both dryer and washer with a variable cost of $160 for the dryer and $330 for the washer. Determine how many days will be required until the company starts making a profit for the washers and the dryers. Use $198 and $500 as selling prices for the dryer and the washer, respectively.

Answer 1

a. Let W = number of washers, and D = number of dryers We can write 5 equations describing the profit and constraints due to capacity:





Graph shows constraint equations without profit.



b. The optimum amount of washers and dryers can be found by considering the corners of the polygon as defined by the area of technical feasibility. All data points must fall within the boundaries of the four equations, so consider the intersection of 2 and 5 given by the nearest contained data points (49,130), and 4 and 5 (36,180).



c. The maximum profit can be calculated for the polygon corner data points.

P(49,130) = $4,133

P(36,180) = $4,320

Plot Equation 1 above for profit = $4,320 on the same graph as above. Note that the line must intersect the technical feasibility area.



Graph shows maximum profit is obtained at P(36,180).



d. The breakeven point occurs where revenue exceeds costs. If we plot revenue and costs versus the production days, we get the chart below. Breakeven occurs between the first and second day, hence the second day is profitable.