A $$Juarez$,$ Mexico, manufacturer of roofing supplies has developed monthly forecasts for a family of products. Data for the$6-$month period January to June are presented in the table below. There are $8$ hours of production per day.

$$a$)$ The firm would like to begin development of an aggregate plan. For this$$plan$,$ plan$5,$ the firm wishes to maintain a constant workforce of

$6,$ using subcontracting to meet remaining demand. Evaluate this plan.

Part $2$

To determine whether this plan is$$desirable$,$ first calculate demand per day for each month $($enter your responses rounded to the nearest whole$$number$).$

Table $1$

Month

Production Days

Demand Forecast

Avg Dem Per Prod. Day

$1$

January

$22$

$900$

$41$

$41$

$2$

February

$18$

$700$

$39$

$39$

$3$

March

$21$

$800$

$38$

$38$

$4$

April

$21$

$1,200$

$57$

$57$

$5$

May

$22$

$1,500$

$68$

$68$

$6$

June

$20$

$1,100$

$55$

$55$

Other data

Inventory carrying cost

$$$

$8$ per unit per month

Subcontracting cost per unit

$$$

$12$ per unit

Average pay rate

$$$

$5$ per hour $($$

$40$ per$$day$)$

Overtime pay Rate

$$$

$7$ per hour$($above $8$ hrs per$$day$)$

$$Labor$-$hours per unit

$1\mathrm{.}6$ hrs per unit

Cost of increasing daily production rate$($hiring &$$training$)$

$$$

$300$ per unit

Cost of decreasing daily production rate$($layoffs$)$

$$$

$600$ per unit

Part $3$

The production rate per day

$=$

$30$

$30$ units. $($Enter your response as a whole$$number$.)$

Part $4$

Fill in the table below. $($Enter your responses as whole$$numbers$.)$

$$

Month

Demand

Regular Production

Subcontract

$($Units$)$

$1$

January

$900$

$660$

$660$

$240$

$240$

$2$

February

$700$

$540$

$540$

$160$

$160$

$3$

March

$800$

$630$

$630$

$170$

$170$

$4$

April

$1,200$

$630$

$630$

$570$

$570$

$5$

May

$1,500$

$660$

$660$

$840$

$840$

$6$

June

$1,100$

$600$

$600$

$500$

$500$

Part $5$

The total regular production cost

$=$$

$29,760$

$29,760.($Enter your response as a whole$$number$.)$

Part $6$

The total subcontracting cost

$=$$

$29760$

$29760.($Enter your response as a whole$$number$.)$

Part $7$

Total cost with plan $5=$$

$59520$

$59520.($Enter your response as a whole$$number$.)$

Part $8$

$$b$)$ Juarez has yet a sixth plan. A constant workforce of

$7$ is$$selected$,$ with the remainder of demand filled by subcontracting. Evaluate this plan.

Part $9$

The production rate per day

$=$

enter your response here

units. $($Enter your response as a whole$$number$.)$