Chapter 7 Homework

Problem 14.14.
Mama’s
Stuffin’ is a popular food item during the fall and winter months, but it is
marginal in the spring and summer. Use the following demand forecasts and costs
to determine which of the following production planning strategies is best for
Mama’s Stuffin’:

a. Level production
over the 12 months.
b. Produce
to meet demand each month. Absorb variations in demand by changing the size of
the workforce.
c. Keep the
workforce at its current level. Supplement with overtime
and subcontracting as necessary.

Month

Demand Forecast

March

2000

April

1000

May

1000

June

1000

July

1000

August

1500

September

2500

October

3000

November

9000

December

7000

January

4000

February

3000

Overtime capacity per month

Regular production

Subcontracting capacity per month

Unlimited

Regular production cost

$30 per pallet

Overtime production cost

$40 per pallet

Subcontracting cost

$50 per pallet

Holding cost

$2 per pallet

Beginning workforce

10 workers

Production rate

200 pallets per worker per month

Hiring cost

$5000 per worker

Firing cost

$8000 per worker

Problem 14-10.
Design a
production plan for Mama’s Stuffin’ in Problem 14.4 using linear programming
and Excel Solver.

Problem S14.1.
Barrows
Textile Mills produces two types of cotton clothdenim and corduroy. Corduroy
is a heavier grade of cotton cloth and, as such, requires 7.5 pounds of raw
cotton per yard, whereas denim requires 5 pounds of raw cotton per yard. A yard
of corduroy requires 3.2 hours of processing time; a yard of denim requires 3.0
hours. Although the demand for denim is practically unlimited, the maximum
demand for corduroy is 510 yards per month. The manufacturer has 6500 pounds of
cotton and 3000 hours of processing time available each month. The manufacturer
makes a profit of $2.25 per yard of denim and $3.10 per yard of corduroy. The
manufacturer wants to know how many yards of each type of cloth to produce to
maximize profit.
a.
Formulate
and solve a linear programming model for this problem.
b.
Solve this
model using the graphical method.

Problem S14-2.
The Tycron
Company produces three electrical productsclocks, radios, and toasters. These
products have the following resource requirements:

Resource Requirements

Product

Cost/Unit

Labor Hours/Unit

Clock

$ 7

2

Radio

?10

3

Toaster

??5

2

The
manufacturer has a daily production budget of $2000 and a maximum of 660 hours
of labor. Maximum daily customer demand is for 200 clocks, 300 radios, and 150
toasters. Clocks sell for $15, radios, for $20, and toasters, for $12. The
company desires to know the optimal product mix that will maximize profit.
Formulate
and solve a linear programming model for this problem.Chapter 7 HomeworkProblem 14.14.Mama’s
Stuffin’ is a popular food item during the fall and winter months, but it is
marginal in the spring and summer. Use the following demand forecasts and costs
to determine which of the following production planning strategies is best for
Mama’s Stuffin’:a. Level production
over the 12 months.b. Produce
to meet demand each month. Absorb variations in demand by changing the size of
the workforce.c. Keep the
workforce at its current level. Supplement with overtime
and subcontracting as necessary.MonthDemand ForecastMarch2000April1000May1000June1000July1000August1500September2500October3000November9000December7000January4000February3000Overtime capacity per monthRegular productionSubcontracting capacity per monthUnlimitedRegular production cost$30 per palletOvertime production cost$40 per palletSubcontracting cost$50 per palletHolding cost$2 per palletBeginning workforce10 workersProduction rate200 pallets per worker per monthHiring cost$5000 per workerFiring cost$8000 per workerProblem 14-10.Design a
production plan for Mama’s Stuffin’ in Problem 14.4 using linear programming
and Excel Solver.Problem S14.1.Barrows
Textile Mills produces two types of cotton clothdenim and corduroy. Corduroy
is a heavier grade of cotton cloth and, as such, requires 7.5 pounds of raw
cotton per yard, whereas denim requires 5 pounds of raw cotton per yard. A yard
of corduroy requires 3.2 hours of processing time; a yard of denim requires 3.0
hours. Although the demand for denim is practically unlimited, the maximum
demand for corduroy is 510 yards per month. The manufacturer has 6500 pounds of
cotton and 3000 hours of processing time available each month. The manufacturer
makes a profit of $2.25 per yard of denim and $3.10 per yard of corduroy. The
manufacturer wants to know how many yards of each type of cloth to produce to
maximize profit.a.
Formulate
and solve a linear programming model for this problem.b.
Solve this
model using the graphical method.

Problem S14-2.The Tycron
Company produces three electrical productsclocks, radios, and toasters. These
products have the following resource requirements:Resource RequirementsProductCost/UnitLabor Hours/UnitClock$ 72Radio?103Toaster??52The
manufacturer has a daily production budget of $2000 and a maximum of 660 hours
of labor. Maximum daily customer demand is for 200 clocks, 300 radios, and 150
toasters. Clocks sell for $15, radios, for $20, and toasters, for $12. The
company desires to know the optimal product mix that will maximize profit.Formulate
and solve a linear programming model for this problem.