Calculus III Report

c. Explain how the location of each curve graphed in question 7b would be altered if (1) total fixed cost had been $100

Total cost = (F * T/Q) + (H * Q / 2) = (80 * 200,000 / 10,000) + (1.00 * 10,000/2)

We use $\mathscr{A}_I \subseteq \Im_I$ to denote the collection that contains an optimal solution at node

I can be sure that I solve the equation correctly because I know line BF is 180 and I have the measurement of <AHB and <GHF and the work are shown above how I got the answer for A.

Unit contribution = Unit Price – Unit Variable Cost = $1.80 – $1.40 = $0.40

If Marlene Herbert were to discontinue place mats, he would miss $270,000 that will go toward Mendel paper company fixed cost. The company currently has a plant overhead that is estimated at $420,000 for the quarter. In addition to the fixed plant overhead, the plant incurs fixed selling and administrative expenses per quarter of $118,000. This draws the company to a total fixed cost of $538,000. If Marlene Herbert were to discontinue the second highest contributor to the fixed cost, he would need to increase the volume of computer paper and lower material cost to help pull the contribution margin of the lowest product up to help support the lost of a whole product line.

18) In a maximal flow problem, each node in the network is associated with a decision variable.

| | | | | | | | | | | | | |75000 | |100000 | |125000 | |150000 | |175000 | |200000 | | |  | |  | |  | |  | |  | |  | |Direct Labor |4.00 |  |3.90 |  |3.80 |  |3.70 |  |3.80 |  |4.00 | |Material |2.00

Wall Décor might have a business problems in the near future if the company still allocates manufacturing overhead based on the cost of the prints. From the question No.5, the result shown over costing and under costing for unframed prints and framed prints, respectively. Calculating by this method resulting in the cost of unframed print is much higher than it should be and the cost of framed

right-hand side and divide both sides by P, we can rewrite this equation and find the price-cost

The product my business has chose to produce is water bottles. After some research it can be said that the typical production cost of one water bottle unit is $20. Total fixed costs for my company including rent and utilities are $4000 per month. Given these numbers a linear cost function for my product can be constructed; C(x) = 20x + 4000. In this equation x represents water bottles produced each month at a price of $20 along with $4000 of total fixed costs. An estimated total cost per month can then be determined of $120,000 looking at what the company can afford. Using the cost function C(x), we can plug in 120,000 to then determine the number of water bottles produced each month, which will be x. The beginning equation is C(120000) = 20x + 4000, begin by subtracting 4000 from each side leaving us with 116000 = 20x then divide both sides of the equation by 20 to get a final answer of x = 5800. This is the number of bottles produced each month.

a. Investigate the original calculation of Setup Cost (denoted by “S” in the case), is there

PART A – Linear Programming 1 a) Linear Programing Model Decision Variables: Let x = acres of watermelon Let y = acres of cantaloupe Objective Function: Maximize Z = 390x + 1300y – 5(20x + 15y) + 5(2x + 2.5y) = 270x + 300y – 100x + 75y + 10x + 12.5y = 256x + 284.5y where Z = total profit 390x = profit from watermelons 1300y = profit from cantaloupe 5(20x + 15y) = cost of fertilizer 5(2x + 2.5y) = cost of labour Identification of Constants: Maximize Z = 256x + 284.5y

Where X ⊂ Rn is a subset, and f , gi: X → R, i ∈ I = {1, 2, . . . , m} are continuously differentiable functions. Let X0= {x ∈ X|gi(x) ≤ 0, i = 1, 2, . . . , m} be the feasible solution set. Here we assume that X0 is nonempty. The penalty function method provides an important approach to solving (P), and it has attracted many researchers in both theoretical and practical aspects (see e.g. [1,8,9,11,12,18,25]). In 1967, Zangwill [25] first proposed the classic l1 exact penalty function:

sales volume ⎞ ⎛ unit variable sales volume ⎞ ⎛ unit fixed ⎜ ⎟ −⎜ ⎟ − ⎜ sales price × ⎟ ⎜ expense × ⎟ expenses = 0 in units ⎠ ⎝ in units ⎠ ⎝