$1)$ A sales budget is given below for one of the products manufactured by the Key Co$.$:

January $21,000$ units

February $36,000$ units

March $61,000$ units

April $41,000$ units

May $31,000$ units

June $25,000$ units

The inventory of finished goods at the end of each month should equal $20\%$ of the next month's sales. However, on December $31,$ the finished goods inventory totalled only $4,000$ units.

Each unit of product requires three specialized electrical switches. Since the production of these specialized switches by Key's suppliers is sometimes irregular, the company has a policy of maintaining an ending inventory at the end of each month equal to $30\%$ of the next month's production needs. This requirement had been met on January $1$ of the current year.

Required:

Prepare a budget showing the quantity of switches to be purchased each month for January, February, and March, and in total for the quarter.

$2)$ The following overhead data are for a department in a large company.

Activity Costs Incurred Static Budget

Activity Level $($in units$)250220$

Variable costs:

Indirect materials $$8,745$ $$7,634$

Power $$2,065$ $$1,738$

Fixed costs:

Supervision $$1,560$ $$1,600$

Rent $$7,210$ $$7,300$

Required:

Prepare a report that would be useful in assessing how well costs were controlled in this department.

$3)$ Glocker Company makes three products in a single facility. These products have the following unit product costs:

Products

A B C

Direct materials $$10\mathrm{.}90$ $$15\mathrm{.}80$ $$8\mathrm{.}00$

Direct labour $12\mathrm{.}5012\mathrm{.}609\mathrm{.}90$

Variable manufacturing overhead $2\mathrm{.}401\mathrm{.}201\mathrm{.}40$

Fixed manufacturing overhead $11\mathrm{.}607\mathrm{.}207\mathrm{.}80$

Unit product cost $$37\mathrm{.}40$ $$36\mathrm{.}80$ $$27\mathrm{.}10$

Additional data concerning these products are listed below.

Products

A B C

Mixing minutes per unit $2\mathrm{.}001\mathrm{.}000\mathrm{.}50$

Selling price per unit $$55\mathrm{.}80$ $$54\mathrm{.}60$ $$43\mathrm{.}10$

Variable selling cost per unit $$2\mathrm{.}10$ $$1\mathrm{.}40$ $$1\mathrm{.}90$

Monthly demand in units $2,0001,0003,000$

The mixing machines are potentially a constraint in the production facility. A total of $5,900$ minutes are available per month on these machines.

Direct labour is a variable cost in this company.

Required:

a$)$ How many minutes of mixing machine time would be required to satisfy demand for all four products?

b$)$ How much of each product should be produced, rounded to the nearest whole unit, to maximize operating income

c$)$ Up to how much should the company be willing to pay, rounded to the nearest whole cent, for one additional minute of mixing machine time if the company has made the best use of the existing mixing machine capacity?