MANUFACTURING. Kelly Industries manufactures two different structural support products used in the construction of large boats and ships. The two products, the Z345 and the W250, are produced from specially treated zinc and iron and are produced in both standard and industrial grades. Kelly nets a profit of $400 on each standard Z345 and $500 on each standard W250. Industrial models net a 40% premium

Each week, up to 2500 pounds of zinc and 2800 pounds of iron can be treated and made available for production. The following table gives the per unit requirements (in pounds) for each model.

Z345 W250

Standard Industrial Standard Industrial

Zinc 25 46 16 34

Iron 50 30 28 12

Kelly has a contract to supply a combined total of at least 20 standard or industrial Z345 supports to Calton Shipbuilders each week. Company policy mandates that at least 50% of the production must be industrial models and that neither Z345 models nor W250 models can account for more than 75% of weekly production. By adhering to this policy, Kelly feels, it can sell all the product it manufactures.

a. Determine a weekly production plan for Kelly Industries. What interpretation can you give to the fractional values that are part of the optimal production quantities?

b. What proportion of the production are W250 models? What does that tell you about how the profit will be affected if the 75% limit is loosened or eliminated?

c. State whether you should buy additional shipments of zinc, should they become available at the following premiums above zinc’s normal cost.

i. 100 pounds for $1500

ii. 100 pounds for $2600

iii. 800 pounds for $10,000