Sa

25,000 5,000

7,500 7,500

And the total profit contribution per week is n = $11.50(30,000) + $23(15,000) = $690,000

C. Solution values can be interpreted as follows:

Qa

= 30,000

Qb

= 15,000

Sa

= 5,000

SB

= 7,500

SR

=0

SW

=0

n

= $690,000

Optimal production of Low Calorie bread is 30,000 cases per week. Optimal production of High Fiber bread is 15,000 cases per week. The production of Low Calorie bread exceeds the 25,000 case minimum by 5,000 units.

The production of High Fiber bread exceeds the 7,500 case minimum by 7,500 units.

The minimally acceptable 2:1 ratio of Low Calorie:High Fiber bread is produced.

All worker hours are utilized; no excess worker capacity exists. Maximum weekly profit contribution given constraints

D. $7.67 per case. In the initial problem, there are two feasible solutions that are at the corners of the feasible space that is furthest away from the origin. The optimal solution point X entails production of QA = 30,000, QB = 15,000 and n = $690,000. An inferior cornerpoint solution is at point Y where QA = 40,000, QB = 7,500 and n = $632,500.

Analytically, point X is preferred to point Y because it emphasizes production of the higher-margin High Fiber bread. Graphically, point X is preferred to point Y because the slope of the isoprofit line (equal to -2) is "steeper" than the slope of the worker hours constraint (4) (equal to -1.33). If the slope of the isoprofit line became slightly less negative than the worker hours constraint, then the optimal production level would shift from point X to point Y.

In general, the isoprofit line formula is n = KAQA + KBQB

QA = (n/nA) - (nB/nA)QB In this specific case, the isoprofit line is

To intersect the feasible space at point Y rather than point X, the slope of this line would have to become slightly less negative than -1.33. To solve for the required level for nB, note that if

Given a price of High Fiber bread of $40 per unit, a profit contribution of $15.33 implies variable costs per unit of $24.67 because nB = Price - Variable costs per unit = $40 - $24.67 = $15.33

Therefore, to change the optimal production point from point X to point Y, variable costs per unit on High Fiber bread would have to rise by at least $7.67 per unit:

Change in variable costs = New level - Initial level

Interstate Bakeries, Inc., LP graph

Cases of Low Calorie bread, QA

Interstate Bakeries, Inc., LP graph

Cases of Low Calorie bread, QA

Cases of High Fiber bread, QB

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