A. Estimation of cost structure based on intuition of the management.
1. Material costs are all variable.
2. Direct labor costs are all variable.
3. Factory overheads have initially been estimated as 250% of direct labor costs. However, the management estimates 20% of the overheads to be variable. Thus the variable component of overheads is (250 X .2 = 50)% of direct labor costs.
4. Selling & administrative expense is 15% of sales (selling price for calculations per unit) of which, half is variable. Thus 7.5% of direct labor costs is variable.
We can make a table of contributions & profits for all three products as follows:
We know the constraints:
1. Max demand for A, B & C is 130,000, 50,000 and 50,000, respectively.
2. Departments 1 and 2 cannot exceed 67,000 and 63,000 capacity respectively.
3. To maintain loyal customers, we must supply at least 80,000, 32,000 and 12,000 units of A, B & C, respectively.
4. The total production capacity of the whole factory cannot exceed last year’s production i.e. 160,000.
We can formulate our objective function for contributions & quantity as follows:
Objective Function: max (8.5A + 4B + 5.9C)
With constraints: 1 A <= 130,000, B <= 50,000 and C <= 50,000.
2 2A + 4B + 3C <= 67,000 and 4A + 8B + 1.33C <= 63,000.
3 A >= 80,000, B >= 32,000 and C >= 12,000.
4 A + B + C <= 160,000.
By producing 101,000 units of A, 0 units of B and 50,000 units of C, Bayview can maximize it’s contribution (1,153,500).
B. Estimation of Cost Structure through regression.
1. Regression of total factory overhead on total direct labor cost would give us fixed component of overheads as intercept and variable component as the slope.
The slope of 0.506 (=0.5) tells us that variable overheads are HALF of labor cost. This is in perfect agreement with the intuitive result obtained in part A of the analysis.
2. Regression of total mktg (sales) & admin. expenses on total sales would give us fixed component... [continues]
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