Slavin Corporation manufactures two products, Alpha and Delta. Each product requires time on a single machine. The machine has a monthly capacity of $500$ hours. Total market demand for the two products is limited to $170$ units $($each$)$ monthly. Slavin is currently producing $110$ Alphas and $110$ Deltas each month. Cost and machine$-$usage data for the two products are shown in the following table, which Slavin managers use for planning purposes.

Alpha Delta Total

Price $ $125$ $ $155$

Less variable costs per unit

Material $1732$

Labor $2335$

Overhead $1414$

Contribution margin per unit $ $71$ $ $74$

Fixed costs

Manufacturing $ $7,400$

Marketing and administrative $ $4,400$

$ $11,800$

Machine hours per unit $2\mathrm{.}02\mathrm{.}5$

Machine hours used $495$

Machine hours available $500$

Quantity produced $110110$

Maximum demand $170170$

Profit $ $4,150$

Required:

a$.$ What is the optimal production schedule for Slavin? In other words, how many Alphas and Deltas should the company produce each month to maximize monthly profit?

b$.$ If Slavin produces at the level found in requirement $($a$),$ how much will monthly profit increase over the current production schedule?