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This is the variable cost of $10.50 for B18 plus the unavoidable fixed cost of $44,000 divided by Stewart's annual requirement of 11,000 units of B18. Since the $44,000 in fixed cost is unavoidable and will continue whether the equipment is used or not, this fixed cost is not relevant to this decision and should not be included. This question asks what is the maximum amount Stewart would be willing to pay an outside supplier for B18. The alternative to buying some of its requirements of B18 outside is buying some of its requirements of B12 outside. If the additional cost to purchase B18 outside were to increase above the additional cost to purchase B12 outside, then Stewart would choose to purchase the B12 outside instead. Thus, we need to consider the additional cost per machine hour that Stewart would have to pay for the B12 to be the upper limit for additional cost per machine hour to pay for the B18. (Because at a price for B18 that is above that additional cost, Stewart will purchase the B12 outside instead.)
This is the total variable cost per unit ($3.75 + $4.50 + $2.25). If the company had idle capacity and could produce all it needed, this would be the most it would pay to an outside supplier. However, Stewart does not have adequate capacity to produce all that it needs, and so the company must obtain some of its components from an outside supplier. This question asks what is the maximum amount Stewart would be willing to pay an outside supplier for B18. The alternative to buying some of its requirements of B18 outside is buying some of its requirements of B12 outside. If the additional cost to purchase B18 outside were to increase above the additional cost to purchase B12 outside, then Stewart would choose to purchase the B12 outside instead. Thus, we need to consider the additional cost per machine hour that Stewart would have to pay for the B12 to be the upper limit for additional cost per machine hour to pay for the B18. (Because at a price for B18 that is above that additional cost, Stewart will purchase the B12 outside instead.)
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The first thing needed is to determine which component should receive priority on the limited resource of machine hours. To do this, we need to calculate the loss per unit of the constrained resource if B12 is purchased outside versus being manufactured in-house, and the loss per unit of the constrained resource if B18 is purchased outside versus being manufactured in-house. To do this, we total all of the variable costs per unit ($2.25 + $4.00 + $2.00 = $8.25 for B12, and $3.75 + $4.50 + $2.25 = $10.50 for B18). We then subtract the quoted price from the supplier for each of the components from their variable costs to produce in-house. This gives us $8.25 ? $11.25, or $(3.00) for B12, and $10.50 ? $13.50, or $(3.00) for B18. The cost per component to purchase the parts from the outside supplier is $3.00 for both components. Then, we divide each of those costs per component by the number of machine hours required to produce each product in-house. The result is the cost per machine hour for each component, which is the cost per unit of the constrained resource for each component. This gives us $(3.00) ÷ 2.5, or $(1.20) for B12 and $(3.00) ÷ 3.0, or $(1.00) for B18. Since the cost per unit of the constrained resource (machine hours) is higher to purchase B12 outside than it is to purchase B18 outside ($1.20 for B12 versus $1.00 for B18), Stewart should produce all of the B12 that it needs in-house and as much B18 as it can produce in the remaining machine time. The amount that it needs of B18 which it cannot produce itself should be purchased outside. This will minimize the additional cost that will result from having to purchase some of its components from an outside supplier. This will mean producing 8,000 units of B12, requiring 2.5 machine hours each for a total of 20,000 hours; and in the 21,000 hours left, producing 21,000 ÷ 3, or 7,000 units of B18; and purchasing the remainder of the B18 units needed. Since the $44,000 in fixed costs is unavoidable and will continue whether the equipment is used or not, this fixed cost is not relevant to this decision and should not be included in any of the calculations. This question asks what is the maximum amount Stewart would be willing to pay an outside supplier for B18. The alternative to buying some of its requirements of B18 outside is buying some of its requirements of B12 outside. If the additional cost to purchase B18 outside were to increase above the additional cost to purchase B12 outside, then Stewart would choose to purchase the B12 outside instead. Thus, we need to consider the additional cost per machine hour that Stewart would have to pay for the B12 to be the upper limit for additional cost per machine hour to pay for the B18. (Because at a price for B18 that is above that additional cost, Stewart will purchase the B12 outside instead.) Since B18 requires 3 hours of machine time to produce one unit, the maximum amount that Stewart would pay an outside supplier for B18 would include $1.20 × 3, or $3.60 (the loss per machine hour to produce one unit of B12 × the number of hours required to produce one unit of B18). Therefore, the total cost that Stewart would pay an outside supplier for B18 would be $10.50 (the company's variable cost per unit) plus a $3.60 cost to purchase a unit of B12 outside, for a total of $14.10.