The operations manager of a mail order house purchases double (d) and twin (t) beds for resale. each double bed costs $500 and requires 100 cubic feet of storage space. each twin bed costs $300 and requires 90 cubic feet of storage space. the manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. profit for each double bed is $300 and for each twin bed is $150. the manager’s goal is to maximize profits. what is the weekly profit when ordering the optimal amounts?

The weekly profit when ordering the optimal amounts is $42,000

Step-by-step explanation:

Cost of one double bed = $500, storage space of one double bed = 100 cubic feet

Cost of one twin bed = $300, storage space of one twin bed = 90 cubic feet

Capital for the week = $75,000

Storage capacity of warehouse = 18,000 cubic feet

Profit for each double bed = $300

Profit for each twin bed = $150

Since the capital for the week is $75,000 and the storage capacity of the warehouse is 18,000 cubic feet, the optimal amounts the operations manager can order is 90 double bed and 100 twin bed

Cost of ordering 90 double bed = 90 × $500 = $45,000

Storage space = 90 × 100 cubic feet = 9000 cubic feet

Cost of ordering 100 twin bed = 100 × $300 = $30,000

Storage space = 100 × 90 cubic feet = 9,000 cubic feet

Total cost = $45,000 + $30,000 = $75,000

Total storage space = 9,000 cubic feet + 9,000 cubic feet = 18,000

Therefore, weekly profit = (90 ×$300) + (100 × $150) = ($27,000 + $15,000) = $42,000

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places