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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
Profit per Unit
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?

Lyn Linh
Management Science

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>=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

Lyn Linh
Management Science

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.

Management Science

Which of the following functions is nonlinear?
A)4X + 2Y + 7Z
B)-4X + 2Y
C)4X + (1/2)Y + 7Z
E)4X/Y + 7Z
F)None of the above

Management Science
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