5) A computer retail store sells two types of flat screen monitors: 17 inches and 19 inches, with a profit
contribution of $300 and $250, respectively. The monitors are ordered each week from an outside
supplier. As an added feature, the retail store installs on each monitor a privacy filter that narrows the
viewing angle so that only persons sitting directly in front of the monitor are able to see on-screen data.
Each 19″ monitor consumes about 30 minutes of installation time, while each 17″ monitor requires
about 10 minutes of installation time. The retail store has approximately 40 hours of labor time
available each week. The total combined demand for both monitors is at least 40 monitors each week.
How many units of each monitor should the retail store order each week to maximize its weekly profits
and meet its weekly demand?
6) Creatine and protein are common supplements in most bodybuilding products. Bodyworks, a
nutrition health store, makes a powder supplement that combines creatine and protein from two
ingredients (X1 and X2). Ingredient X1 provides 20 grams of protein and 5 grams of creatine per
pound. Ingredient X2 provides 15 grams of protein and 3 grams of creatine per pound. Ingredients X1
and X2 cost Bodyworks $5 and $7 per pound, respectively. Bodyworks wants its supplement to contain
at least 30 grams of protein and 10 grams of creatine per pound and be produced at the least cost.
Determine what combination will maximize profits.
7) A furniture store produces beds and desks for college students. The production process requires
assembly and painting. Each bed requires 6 hours of assembly and 4 hours of painting. Each desk
requires 4 hours of assembly and 8 hours of painting. There are 40 hours of assembly time and 45 hours
of painting time available each week. Each bed generates $35 of profit and each desk generates $45 of
profit. As a result of a labor strike, the furniture store is limited to producing at most 8 beds each week.
Determine how many beds and desks should be produced each week to maximize weekly profits.
8) An ice cream shop sells single scoop ice cream cones that come in three flavors: chocolate only,
vanilla only, and chocolate-vanilla twist. The cones are prepackaged and sold to a supermarket daily.
The ingredients used along with the minimum demand of each flavor are shown as follows:
Ice Cream Flavor
Chocolate Vanilla Chocolate-Vanilla
Ingredient:
Chocolate 4 oz. 0 oz. 3 oz.
Vanilla 0 oz. 4 oz. 2 oz.
Min daily demand: 20 scoops 15 scoops 10 scoops
Each day, 40 pounds of chocolate and 38 pounds of vanilla are supplied to the ice cream shop from an
outside vendor. The chocolate, vanilla, and chocolate-vanilla twist each yield a profit of $2.00, $2.50,
and $3.00 per cone, respectively. How many chocolate, vanilla, and chocolate-vanilla twist cones must
prepackage daily to maximize daily profits?
9) A company manufactures four products A, B, C, and D that must go through assembly, polishing, and
packing before being shipped to a wholesaler. For each product, the time required for these operations is
shown below (in minutes) as is the profit per unit sold.
Product Assembly Polish Pack Profit ($)
A 2 3 2 1.50
B 4 2 3 2.50
C 3 3 2 3.00
D 7 4 5 4.50
The company estimates that each year they have 1667 hours of assembly time, 833 hours of polishing
time and 1000 hours of packing time available. How many of each product should the company make
per year to maximize its yearly profit?
10) Suppose that a farmer has 5 acres of land that can be planted with either wheat, corn, or a
combination of the two. To ensure a healthy crop, a fertilizer and an insecticide must be applied at the
beginning of the season before harvesting. The farmer currently has 100 pounds of the fertilizer and 150
pounds of the insecticide at the beginning of the season. Each acre of wheat planted requires 10 pounds
of the fertilizer and 12 pounds of the insecticide. Each acre of corn planted requires 13 pounds of the
fertilizer and 11 pounds of the insecticide. Each acre of wheat harvested yields a profit of $600, while
each acre of corn harvested yields $750 in profit. What is the optimal allocation for the crops that
maximizes the farmer’s profit?
11) A carpenter makes tables and chairs. Each table can be sold for a profit of $50 and each chair for a
profit of $30. The carpenter works a maximum of 40 hours per week and spends 5 hours to make a table
and 2 hours to make a chair. Customer demand requires that he makes at least twice as many chairs as
tables. The carpenter stores the finished products in his garage, and there is room for a maximum of 6
furniture pieces each week. Determine the carpenter’s optimal production mix.
12) A bank is attempting to determine where its assets should be allocated in order to maximize its
annual return. At present, $750,000 is available for investment in three types of mutual funds: A, B, and
C. The annual rate of return on each type of fund is as follows: fund A, 15%; fund B, 12%; fund C; 13%.
The bank’s manager has placed the following restrictions on the bank’s portfolio:
• No more than 20% of the total amount invested may be in fund A.
• The amount invested in fund B cannot exceed the amount invested in fund C.
Determine the optimal allocation that maximizes the bank’s annual return.
13) A warehouse stocks five different products, A, B, C, and D. The warehouse has a total of 100,000
square feet of floor space available to accommodate all the products that it inventories. The monthly
profit per square foot for each product is as follows:
Product Profit per square foot
A $4.50
B $3.00
C $2.75
D $3.75
Each product must have at least 10,000 ft2, and no single product can have more than 25% of the total
warehouse space. The warehouse manager wants to know the floor space that should be allocated to
each product to maximize profit.
14) A company that is introducing a new product would like to generate maximum market exposure.
The marketing department currently has $100,000 of advertising budget for the year and is considering
placing ads in three media: radio, television, and newspapers. The cost per ad and the exposure rating
are as follows:
Cost/ad Exposure/ad
Radio $10,000 30,000 individuals
Television $25,000 50,000 individuals
Newspaper $5000 20,000 individuals
The marketing department would like to place twice as many radio ads as television ads. They also
would like to place at least 4 ads in each advertising media. What is the optimal allocation to each
advertising medium to maximize audience exposure?
15) A meat packing store produces a dog food mixture that is sold to pet retail outlets in bags of 10
pounds each. The food mixture contains the ingredients turkey and beef. The cost per pound of each of
these ingredients is as follows:
Ingredient Cost/pound
Turkey $2.00
Beef $5.50
Each bag must contain at least 5 pounds of turkey. Moreover, the ratio of turkey to beef must be at least
2 to 1. What is the optimal mixture of the ingredients that will minimize total cost?
16) A company can decide how many additional labor hours to acquire for a given week. Subcontractors
will only work a maximum of 20 hours a week. The company must produce at least 200 units of product
A, 300 units of product B, and 400 units of product C. In 1 hour of work, worker 1 can produce 15 units
of product A, 10 units of product B, and 30 units of product C. Worker 2 can produce 5 units of product
B, 20 units of product B, and 35 units of product C. Worker 3 can produce 20 units of product A, 15
units of product B, and 25 units of product C. Worker 1 demands a salary of $50/hr, worker 2 demands
a salary of $40/hr, and worker 3 demands a salary of $45/hr. The company must choose how many hours
they should hire from each worker to meet their production requirements and minimize labor cost.