Corporation M produces SMART X product. Currently Corporation M is working at full production capacity producing $13,000$ units of SMART X$.$ Manufacturing cost per unit for SMART X is:

Direct materials $ $10$

Direct manufacturing labor $2$

Manufacturing overhead $14$

Total manufacturing cost $ $26$

Based on this production level, fixed manufacturing overhead cost per unit is $$6$ and the rest of the manufacturing overhead cost is considered variable manufacturing cost. The selling price per unit is $$52$ and the operating cost per unit, considered all variable, is $$4.$

One customer is wondering whether Corporation M will be willing to produce for him $3,500$ units of SMART Y that resembles SMART X but with slight modification of SMART X$,$ and would require the same manufacturing process. The customer has offered to pay Corporation M $$40$ for a unit of SMART Y and pay half of the operating cost per unit.

Required

$1.$ Assume that no overtime is worked, would you recommend Corporation M to accept the customer$$s request? Why?

$2.$ Company N a competitor of Corporation M has offered to produce $3,500$ units of SMART X for Corporation M so that Corporation M may accept the customer$$s request. That is$,$ if Corporation M accepts Company$$s N offer, Corporation M would manufacture $9,500$ units of SMART X and $3,500$ units of SMART Y and purchase $3,500$ units of SMART X from Company N$.$ Company N would charge Corporation M $$36$ per unit to manufacture SMART X$.$ On the basis of financial considerations alone, should CORPORATION M accept Company$$s N offer? Show your calculations.

$3.$ Suppose Corporation M had been working at less than full capacity, producing $9,500$ units of SMART X$,$ at the time the customer$$s offer was made. Calculate the minimum price Corporation M should accept for SMART Y under these conditions. $($Ignore the previous $$40$ selling price.$)$