Problems

1. Suppose our drug company can purchase up to 500 hours of labor at $1 more per hour than current labor costs. How can we maximize profit?

2. At a chip manufacturing plant, four technicians (A, B, C, and D) produce three products (Products 1, 2, and 3). This month, the chip manufacturer can sell 80 units of Product 1, 50 units of Product 2, and at most 50 units of Product 3. Technician A can make only Products 1 and 3. Technician B can make only Products 1 and 2. Technician C can make only Product 3. Technician D can make only Product 2. For each unit produced, the products contribute the following profit: Product 1, $6; Product 2, $7; and Product 3, $10. The time (in hours) each technician needs to manufacture a product is as follows:

   Open table as spreadsheet

   Product	Technician A	Technician B	Technician C	Technician D
   1	2	2.5	Cannot do	Cannot do
   2	Cannot do	3	Cannot do	3.5
   3	3	Cannot do	4	Cannot do

   Each technician can work up to 120 hours per month. How can the chip manufacturer maximize its monthly profit? Assume a fractional number of units can be produced.

3. A computer manufacturing plant produces mice, keyboards, and video game joysticks. The per-unit profit, per-unit labor usage, monthly demand, and per-unit machine-time usage are given in the following table:

   Open table as spreadsheet

   	Mice	Keyboards	Joysticks
   Profit/unit	$8	$11	$9
   Labor usage/unit	.2 hour	.3 hour	.24 hour
   Machine time/unit	.04 hour	.055 hour	.04 hour
   Monthly demand	15,000	27,000	11,000

   Each month, a total of 13,000 labor hours and 3000 hours of machine time are available. How can the manufacturer maximize its monthly profit contribution from the plant?

4. Resolve our drug example assuming that a minimum demand of 200 units for each drug must be met.

5. Jason makes diamond bracelets, necklaces, and earrings. He wants to work a maximum of 160 hours per month. He has 800 ounces of diamonds. The profit, labor time, and ounces of diamonds required to produce each product are given below. If demand for each product is unlimited, how can Jason maximize his profit?

   Open table as spreadsheet

   Product	Unit profit	Labor hours per unit	Ounces of diamonds per unit
   Bracelet	$300	.35	1.2
   Necklace	$200	.15	.75
   Earrings	$100	.05	.5