Question

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 115 Alphas and 115 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 17 32 Labor 23 35 Overhead 14 14 Contribution margin per unit $ 71 $ 74 Fixed costs Manufacturing $ 7,400 Marketing and administrative $ 4,400 $ 11,800 Machine hours per unit 2.0 2.5 Machine hours used 495 Machine hours available 500 Quantity produced 115 115 Maximum demand 170 170 Profit $ 4,875.

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?

Answer 1

1)Hours required to meet maximum demand :[170*2]Alpha +[170*2.5] Delta

                  = 340+ 425

                  = 765 hours

since hours required is more than hours available (500) ,we will produce that product first that yield maximum profit.

	Alpha	Delta
contribution per unit	71	74
machine hours per unit	2	2.5
contribution per hour	71/2= 35.5	74/2.5= 29.6
Ranking based on highest contribution	1	2

we will meet maximum demand of alpha first and then produce delta with machine hours available.

Product	units produced	machine hours per unit	Total machine hours used	Remaining machine hours
Alpha	170`	2	340	500-340= 160
Delta	160/2.5= 64	2.5	160	0

we will produce 170units of alpha and 64 units of delta to maximize profit.

2)Total contribution from optimal production :[170units *71contribution per unit]Alpha+[64*74]Delta

             = 12070+ 4736

            = 16806

Profit = contribution -fixed cost

      = 16806 -11800

       = 5006

Increase in profit =profit from optimal production -current profit

              = 5006- 4875

              = 131