Exercise $9\mathrm{.}1$ Exercise $9\mathrm{.}1$

Lavare, located in the Chicago suburbs, is a major manufacturer of stainless$-$steel sinks$.$ Lavare is in the

middle of the demand and supply planning exercise for the coming year. Anticipated monthly demand

from distributors over the $12$ months is shown in Table $9-4.$ Capacity at Lavare is governed by the

number of machine operators it hires. The firm works $20$ days a month, with a regular operating shift of

eight hours per day. Any time beyond that is considered overtime. Regular$-$time pay is $$20$ per hour and

overtime is $$25$ per hour. Overtime is limited to $20$ hours per month per employee. The plant currently

has $250$ employees. Each sink requires two hours of labor input. It costs $$3$ to carry a sink in inventory

for a month. Materials cost per sink is $$40.$ Sinks are sold to distributors at a price of $$125$ each. We

assume that no stockouts are allowed and the starting inventory entering January is $5,000$ units and the

desired ending inventory in December is also $5,000$ units. Market research has indicated that a

promotion dropping prices by $1$ percent in a given month will increase sales in that month by $20$ percent

and bring forward $10$ percent demand from each of the following two months. Thus, a $1$ percent drop in

price in March increases sales in March by $3,000(=0\mathrm{.}2*15,000)$ and shifts $1,800(=0\mathrm{.}1*18,000)$ units

in demand from April and $2,500(=0\mathrm{.}1*25,000)$ units from May forward to March.

a$.$ What is the optimal production plan for the year if we assume no promotions?

b$.$ What is the annual profit from this plan?

c$.$ What is the cost of this plan?

d$.$ Is it better to promote in April or July?

e$.$ How much increase in profit can be achieved as a result?

f$.$ If sinks are sold for $$250$ instead of $$125,$ does the decision about the timing of the promotion

change? Why?

TABLE $9-4$ Anticipated Monthly Demand at Lavare Input Data

Demand Forecast

Costs

hours

Lavare, located in the Chicago suburbs, is a major manufacturer of stainless$-$steel sinks$.$ Lavare is in the

middle of the demand and supply planning exercise for the coming year. Anticipated monthly demand

from distributors over the $12$ months is shown in Table $9-4.$ Capacity at Lavare is governed by the

number of machine operators it hires. The firm works $20$ days a month, with a regular operating shift of

eight hours per day. Any time beyond that is considered overtime. Regular$-$time pay is $$20$ per hour and

overtime is $$25$ per hour. Overtime is limited to $20$ hours per month per employee. The plant currently

has $250$ employees. Each sink requires two hours of labor input. It costs $$3$ to carry a sink in inventory

for a month. Materials cost per sink is $$40.$ Sinks are sold to distributors at a price of $$125$ each. We

assume that no stockouts are allowed and the starting inventory entering January is $5,000$ units and the

desired ending inventory in December is also $5,000$ units. Market research has indicated that a

promotion dropping prices by $1$ percent in a given month will increase sales in that month by $20$ percent

and bring forward $10$ percent demand from each of the following two months. Thus, a $1$ percent drop in

price in March increases sales in March by $3,000(=0\mathrm{.}2*15,000)$ and shifts $1,800(=0\mathrm{.}1*18,000)$ units

in demand from April and $2,500(=0\mathrm{.}1*25,000)$ units from May forward to March.

a$.$ What is the optimal production plan for the year if we assume no promotions?

b$.$ What is the annual profit from this plan?

c$.$ What is the cost of this plan?

d$.$ Is it better to promote in April or July?

e$.$ How much increase in profit can be achieved as a result?

f$.$ If sinks are sold for $$250$ instead of $$125,$ does the decision about the timing of the promotion

change? Why?

TABLE $9-4$ Anticipated Monthly Demand at Lavare

Month Demand Month Demand

January $10,000$ July $30,000$

February $12,000$ August $29,000$

March $15,000$ September $23,000$

April $18,000$ October $17,000$

May $25,000$ November $14,000$

June $26,000$ December $11,000$