# Question: The B J Jensen Company specializes in the production of

The B. J. Jensen Company specializes in the production of power saws and power drills for home use. Sales are relatively stable throughout the year except for a jump upward during the Christmas season. Since the production work requires considerable work and experience, the company maintains a stable employment level and then uses overtime to increase production in November. The workers also welcome this opportunity to earn extra money for the holidays.

B. J. Jensen, Jr., the current president of the company, is overseeing the production plans being made for the upcoming November. He has obtained the following data:

*Assuming adequate supplies of materials from the company’s vendors.

However, Mr. Jensen now has learned that, in addition to the limited number of labor hours available, two other factors will limit the production levels that can be achieved this November. One is that the company’s vendor for power supply units will only be able to provide 10,000 of these units for November (2,000 more than his usual monthly shipment). Each power saw and each power drill requires one of these units. Second, the vendor who supplies a key part for the gear assemblies will only be able to provide 15,000 for November (4,000 more than for other months). Each power saw requires two of these parts and each power drill requires one.

Mr. Jensen now wants to determine how many power saws and how many power drills to produce in November to maximize the company’s total profit.

(a) Draw the profit graph for each of these two products.

(b) Use separable programming to formulate a linear programming model for this problem.

(c) Solve the model. What does this say about how many power saws and how many power drills to produce in November?

B. J. Jensen, Jr., the current president of the company, is overseeing the production plans being made for the upcoming November. He has obtained the following data:

*Assuming adequate supplies of materials from the company’s vendors.

However, Mr. Jensen now has learned that, in addition to the limited number of labor hours available, two other factors will limit the production levels that can be achieved this November. One is that the company’s vendor for power supply units will only be able to provide 10,000 of these units for November (2,000 more than his usual monthly shipment). Each power saw and each power drill requires one of these units. Second, the vendor who supplies a key part for the gear assemblies will only be able to provide 15,000 for November (4,000 more than for other months). Each power saw requires two of these parts and each power drill requires one.

Mr. Jensen now wants to determine how many power saws and how many power drills to produce in November to maximize the company’s total profit.

(a) Draw the profit graph for each of these two products.

(b) Use separable programming to formulate a linear programming model for this problem.

(c) Solve the model. What does this say about how many power saws and how many power drills to produce in November?

## Answer to relevant Questions

For each of the following functions, show whether it is convex, concave, or neither. (a) f (x) = 10x – x2 (b) f (x) = x4 + 6x2 + 12x (c) f (x) = 2x3 – 3x2 (d) f (x) = x4 + x2 (e) f (x) = x3 + x4 Consider the following nonlinear programming problem: Maximize Z = 5x1 + x2, subject to 2x12 + x2 ≤ 13 x12 + x2 ≤ 9 and x1 ≥ 0, x2 ≥ 0. (a) Show that this problem is a convex programming problem. (b) Use the ...Consider the quadratic programming example presented in Sec. 13.7. Starting from the initial trial solution (x1, x2) = (5, 5), apply eight iterations of the Frank-Wolfe algorithm. Reconsider the model given in Prob. 13.3-3. (a) If SUMT were to be applied directly to this problem, what would be the unconstrained function P(x; r) to be minimized at each iteration? Consider the following nonconvex programming problem: Maximize f(x) = 3x1 x2 – 2x21 – x32, Subject to and x1 ≥ 0, x2 ≥ 0. (a) If SUMT were to be applied to this problem, what would be the unconstrained function P(x; ...Post your question