# Management Science Homework Help

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. 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

data at the top of the next page.

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.

Maximum Monthly

Production

Profit per Unit

Produced

Regular Time Overtime Regular Time Overtime

Power saws 3,000 2,000 $150 $50

Power drills 5,000 3,000 $100 $75

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

b. Use separable programming to formulate a linear programming model on a

spreadsheet for this problem. Then solve the model. What does this say about

how many power saws and how many power drills to produce in November?

.

The Dorwyn Company has two new products (special kinds of doors and

windows) that will compete with the two new products for the Wyndor Glass Co.

(described in Section 2.1). Using units of hundreds of dollars for the objective

function, the linear programming model in algebraic form shown below has been

formulated to determine the most profitable product mix.

Maximize Profit = 4D + 6W

subject to

D+3W<=8

5D+2W<=14

and

D>=0 ,W>=0

However, because of the strong competition from Wyndor, Dorwyn

management now realizes that the company will need to make a strong

marketing effort to generate substantial sales of these products. In particular, it

is estimated that achieving a pro- duction and sales rate of D doors per week

will require weekly marketing costs of D3 hundred dollars (so $100 for D 5 1,

$800 for D 5 2, $2,700 for D 5 3, etc.). The corresponding market- ing costs for

windows are estimated to be 2 W2 hundred dollars. Thus, the objective function

in the model should be

Profit = 4D + 6W - D^ - 2W^

Dorwyn management now would like to use the revised model to determine the

most profitable product mix.

a. Formulate and solve this nonlinear programming model on a spreadsheet

.

My diet requires that all the food I eat come from one of the four “basic food groups” (chocolate

cake, ice cream, soda, and cheesecake). At present, the following four foods are available for

consumption: brownies, chocolate ice cream, cola, and pineapple cheesecake. Each brownie

costs 50¢, each scoop of chocolate ice cream costs 20¢, each bottle of cola costs 30¢, and each

piece of pineapple cheesecake costs 80¢. Each day, I must ingest at least 500 calories, 6 oz of

chocolate, 10 oz of sugar, and 8 oz of fat. The nutritional content per unit of each food is shown

in Table 1. Formulate a linear programming model that can be used to satisfy my daily

nutritional requirements at minimum cost.

.

Which of the following functions is nonlinear?

A)4X + 2Y + 7Z

B)-4X + 2Y

C)4X + (1/2)Y + 7Z

D)Z

E)4X/Y + 7Z

F)None of the above

.

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