Exercise $11-23($Algo$)$ Special Order; Opportunity Cost $[$LO $11-2]$

Alton Incorporated is working at full production capacity producing $22,000$ units of a unique product. Manufacturing costs per unit for the product are as follows:

Direct materials$ $7$Direct labor$6$Manufacturing overhead$8$Total manufacturing cost per unit$ $21$

The per$-$unit manufacturing overhead cost is based on a $$4$ variable cost per unit and $$88,000$ fixed costs. The nonmanufacturing costs, all variable, are $$8$ per unit, and the sales price is $$34$ per unit.

Sports Headquarters Company $($SHC$)$ has asked Alton to produce $5,400$ units of a modification of the new product. This modification would require the same manufacturing processes. However, because of the nature of the proposed sale, the estimated nonmanufacturing costs per unit are only $$4($not $$8).$ Alton would sell the modified product to SHC for $$24$ per unit.

Required:

Suppose that Alton Incorporated had been working at less than full capacity to produce $17,800$ units of the product when SHC made the offer. What is the minimum price per unit that Alton should accept for the modified product under these conditions?