Oakland Precision Products $($OPP$)$ manufactures and sells a variety of scales for the kitchen and office. OPP sells primarily to kitchenware stores, discount stores, and so on$.$ Two of the scales it produces for kitchen use are the Cook and Baker. The Cook is a basic food scale. The Baker has a greater capacity and special features that facilitate adjusting baking recipes for more or fewer people. The following information is available: Costs per unit Cook $$ Baker $$

$$ Direct materials $$1\mathrm{.}60$ $$14\mathrm{.}40$

$$ Direct labor $0\mathrm{.}803\mathrm{.}20$

$$ Variable overhead $0\mathrm{.}602\mathrm{.}40$

$$ Fixed overhead $8\mathrm{.}0015\mathrm{.}00$

$$ Total cost per unit $$11\mathrm{.}00$ $$35\mathrm{.}00$

$$ Price $$15\mathrm{.}00$ $$45\mathrm{.}00$

$$ Units sold $230,000120,000$

The average wage rate is $$32$ per hour. Variable overhead varies with the quantity of direct labor$-$hours. The plant has a capacity of $20,000$ direct labor$-$hours, but current production uses only $17,750$ direct labor$-$hours.

Required

A nationwide kitchenware chain has offered to buy $30,000$ Cook models and $15,000$ Baker models if the prices are lowered to $$10$ and $$35,$ respectively, per unit. If OPP accepts the offer, how many direct labor$-$hours will be required to produce the additional scales? How much will the profit increase $($or decrease$)$ if OPP accepts this proposal? Prices on regular sales will remain the same.

Suppose that the kitchenware chain has offered instead to buy $50,000$ Cook models at $$10$ per unit and $30,000$ Baker models at $$35.$ This customer will purchase the models only in an all$-$or$-$nothing deal. That is$,$ OPP must provide all $50,000$ units of the Cook model and $30,000$ units of the Baker model or nothing at all. In view of its capacity constraints, OPP will reduce sales to regular customers as needed to fill the special order. How much will the profits change if the order is accepted? Assume that the company cannot increase its production capacity to meet the extra demand, if required.

Answer the question in requirement $($b$)$ assuming instead that the plant can work overtime. Direct labor costs for the overtime production increase to $$45$ per hour. Variable overhead costs for overtime production are $$6$ per hour more than for normal production.