Question 1
The manager of a small firm is considering whether to produce a new product that would require leasing some special equipment at a cost of $20,000 per month. In addition to this leasing cost, a production cost of $ 10 would be incurred for each unit of the product produced. Each unit sold would generate $20 in revenue.Assume a sales forecast has been obtained that indicates that4,000 units of the new products could be sold. This forecast is considered to be quite reliable, but there is considerable uncertainty about the accuracy of the estimates given for the leasing cost, the marginal cost, and the unit revenue. Use the Break-Even Analysismodule in the interactive management science modules to perform the following sensitive analysis on these estimates. Do not use excel for this problem!
- how large can the leasing cost be before this new product ceases to be profitable?
- How large can the marginal production cost be before this new product ceases to be profitable?
- How small can the unit revenue be before this new product ceases to be profitable?
Start with Q = 4000 and find the rest...
1. Q=4000, M=10, Unit Rev = 20
Solve for L
2. Q = 4000 L = 20000 Unit rev = 20 solve for M
3. Q = 4000 L = 20000 M = 10 solve for unit rev
Question 2
Peter likes steaks and potatoes. As a result he decided to go on a steady diet of only these two foods ( plus some liquids and vitamin supplements)for all his meals. Peter realizes that this isn't the healthiest diet so he wants to make sure that he eats the right quantities of the two foods to satisfy some key nutritional requirements. He has obtained the following nutritional and cost information:
IngredientsteakpotatoesDaily requirement (grams)
Carbohydrates515= 50
Protein205= 40
Fat152=60
Cost per serving$4$2
Peter wishes to determine the number of daily servings (may be fractional) of steak and potatoes that will meet these requirement at a minimum cost.